Download GEOMETRY MIDTERM REVIEW PACKET

Name: ______________________
Class: _________________
Date: _________
ID: A
GEOMETRY MIDTERM REVIEW PACKET
Refer to Figure 1.
6
←

→
←

→
Name a point NOT contained in AD or FG .
A K
B A
C H
D D
Refer to Figure 2.
Figure 1
1
2
Name the intersection of lines m and n.
A
3
Figure 2
Name a point NOT contained in lines m, n, or
p.
A A
B K
C H
D D
K
←

→
B
DC
C
B
D
D
Does line p intersect line m or line n? Explain.
A Yes, it intersects both m and n when all
three are extended. B No, the lines do not
meet in this diagram. C Yes, it intersects line
m when both are extended. D Yes, it
intersects line n when both are extended.
4
Name the plane containing lines m and p.
A n
B GFC
C H
D JDB
5
What is another name for line m?
A
line JG
←

→
B
JGB
C
DB
D
7
How many planes are shown in the figure?
A 4
B 3
C 5
D 6
8
How many planes contain points B, C, and A?
A 1
B 2
C 0
D 3
9
Where could you add point M on plane LBD so
that D, B, and M would be collinear?
←

→
A
anywhere on DF
C
anywhere on BL
←

→
B
anywhere on LD
D
anywhere on BD
←

→
line JB
1
←

→
10
How many planes contain points B, L, F, and
D?
A 1
B 0
C 3
D 2
11
Name the intersection of plane KCG and a
plane that contains points L and D.
A plane DGC
B C
C line LC
D line CG
Name: ______________________
ID: A
Use the number line to find the measure.
12
13
PH
A 4.5
RK
A 2
B
B
8
5
C
C
9
7
D
D
Find the coordinates of the midpoint of a
segment having the given endpoints.
–0.5
16
10
Use the Distance Formula to find the distance
between each pair of points.
17
14
Q ÊÁË 1, − 3 ˆ˜¯ , R ÊÁË 11, 5 ˆ˜¯
A Ê
ÁË −1, 8 ˆ˜¯ B ÊÁË −10, − 8 ˆ˜¯
Ê −5, − 4 ˜ˆ
D Á
Ë
¯
C
ÊÁ 6, 1 ˆ˜
Ë
¯
Q ÊÁË −0.4, 2.5 ˆ˜¯ , R ÊÁË 3.5, 1.5 ˆ˜¯
Ê 1.55, 2 ˜ˆ B ÁÊ 1.05, 2.5 ˆ˜
A Á
Ë
¯
Ë
¯
C Ê
ÁË −1.95, 0.5 ˆ˜¯ D ÊÁË −3.9, 1 ˆ˜¯
Name each polygon by its number of sides.
18
A
50
34
B
C
6
D
A
4
D
15
hexagon
pentagon
B
quadrilateral
decagon
octagon
B
dodecagon
C
heptagon
19
A
D
A
50
B
4
C
34
D
6
2
C
nonagon
Name: ______________________
ID: A
24
20
A
D
hexagon B triangle
quadrilateral
C
pentagon
21
A
D
triangle
hexagon
B
quadrilateral
C
pentagon
25
A
D
hexagon B triangle
quadrilateral
C
pentagon
22
A
D
A
D
nonagon
octagon
B
decagon
C
pentagon
octagon
B
quadrilateral
C
hexagon
Name each polygon by its number of sides.
Then classify it as convex or concave and
regular or irregular.
dodecagon
23
26
pentagon, convex, regular B hexagon,
concave, regular C hexagon, convex, regular
D hexagon, convex, irregular
A
A
D
dodecagon
decagon
B
pentagon
C
hexagon
3
Name: ______________________
ID: A
27
30
triangle, convex, regular B triangle,
convex, irregular C triangle, concave,
irregular D quadrilateral, convex, irregular
A
quadrilateral, convex, regular
B quadrilateral, concave, irregular
C pentagon, convex, regular
D quadrilateral,
convex, irregular
A
28
31
A
B
C
D
quadrilateral, convex, regular
quadrilateral, concave, irregular
pentagon, convex, irregular
quadrilateral, convex, irregular
triangle, convex, regular B triangle,
concave, irregular C triangle, convex,
irregular D quadrilateral, convex, irregular
A
32
29
quadrilateral, convex, irregular
B quadrilateral, concave, irregular
C quadrilateral, convex, regular
D pentagon,
convex, regular
A
hexagon, convex, irregular B hexagon,
concave, irregular C hexagon, convex,
regular D heptagon, convex, irregular
A
4
Name: ______________________
ID: A
33
Find the length of each side of the polygon for
the given perimeter.
36
P = 48 cm
A
dodecagon, concave, irregular
B dodecagon, convex, irregular
C decagon,
concave, irregular D decagon, convex, regular
A
37
8 cm
B
6 cm
B
6 mi
C
4 cm
D
3 cm
P = 54 mi
34
A
decagon, convex, irregular B decagon,
concave, irregular C dodecagon, convex,
irregular D dodecagon, concave, irregular
A
38
9 mi
C
3 mi
D
12 mi
P = 60 in. Find the length of each side.
35
pentagon, convex, regular B pentagon,
convex, irregular C hexagon, concave,
irregular D hexagon, convex, irregular
A
11 in., 20 in., 35 in. B 10 in., 18.5 in.,
31.5 in. C 12 in., 21.5 in., 38.5 in. D 10
in., 15 in., 35 in.
A
5
Name: ______________________
39
ID: A
41
P = 72 units. Find the length of each side.
18 units, 18 units, 13 units B 18.66 units,
18.66 units, 13.66 units C 27 units, 27 units,
22 units D 26 units, 26 units, 21 units
A
9 units, 36 units, 4 units, 23 units B 8
units, 33 units, 4 units, 21 units C 9 units, 35
units, 5 units, 23 units D 10 units, 34 units, 6
units, 22 units
A
40
P = 49 units. Find the length of each side.
42
P = 108 mi. Find the length of each side.
P = 100 ft. Find the length of each side.
11 mi, 11 mi, 7 mi, 7 mi B 33 mi, 33 mi,
21 mi, 21 mi C 71 mi, 71 mi, 37 mi, 37 mi
D 35 mi, 35 mi, 19 mi, 19 mi
A
41 ft, 41 ft, 17 ft, 17 ft, 24 ft B 29 ft, 29
ft, 13 ft, 13 ft, 16 ft C 50 ft, 50 ft, 20 ft, 20
ft, 30 ft D 33.5 ft, 33.5 ft, 14.5 ft, 14.5 ft,
19 ft
A
6
Name: ______________________
43
ID: A
Find the circumference of the figure.
P = 56 cm. Find the measure of each side.
46
triangleABC ≅ triangle FDC
measures given are for triangle ABC
A
B
C
D
44
cm,
cm,
cm,
cm,
20 cm, 6 cm, 6 cm, 10 cm, 10 cm
14 cm, 6 cm, 6 cm, 8 cm, 8 cm
30 cm, 9 cm, 9 cm, 17 cm, 17 cm
16 cm, 5 cm, 5 cm, 7 cm, 7 cm
A
D
P = 24 cm. Find the length of each side.
A
C
45
20
14
30
16
8π cm
64π cm
B
16π cm
C
4π cm
47
8 cm, 8 cm, 8 cm B 6 cm, 6 cm, 6 cm
10 cm, 10 cm, 4 cm D 9 cm, 9 cm, 6 cm
about 23.9 in. B about 11.9 in.
7.6 in. D about 45.3 in.
A
P = 36 units. Find the length of each side.
C
about
Find the area of the figure.
48
16 units, 18 units, 14 units B 12 units, 16
units, 8 units C 10 units, 18 units, 8 units
D 12 units, 14 units, 10 units
A
7
A
7.13 cm
2
D
10.8 cm
2
B
5.4 cm
2
C
71.3 cm
2
Name: ______________________
ID: A
49
52
A
75.04 in
2
D
750.4 in
2
A
36π m
2
D
72π m
2
B
17.9 in
2
C
35.8 in
2
53
A
about 22.3 km
2
C
about 89.4 km
2
11 yd
D
about 16.8 km
2
←

→
B
18π m
2
C
12π m
A
2
54
←

→
←
→
2
B
22 yd
2
C
302.5 yd
2
2
8
120
B
60
C
100
D
40
←

→
←

→
←

→
In the figure, m∠RPZ = 95 and TU Ä RQ Ä VW.
Find the measure of angle WSP.
A
D
2
KL Ä NM . Find the measure of angle PRK.
51
30.25 yd
about 44.7 km
In the figure, m∠NML = 120, PQ Ä TU and
←

→
50
A
B
85
B
75
C
95
D
65
Name: ______________________
55
ID: A
Use a protractor to classify the triangle as
acute, equiangular, obtuse, or right.
In the figure, AB Ä CD. Find x and y.
57
A
C
56
x = 32, y = 140
x = 52, y = 140
B
D
A
right
A
obtuse B right C equiangular and obtuse
equiangular and acute
B
acute
equiangular
D
obtuse
58
x = 140, y = 52
x = 38, y = 154
In the figure, p Ä q. Find m∠1.
D
A
D
m∠1 = 61
m∠1 = 64
B
m∠1 = 35
C
m∠1 = 55
Find the measures of the sides of ΔABC and classify the triangle by its sides.
59
C
A ÊÁË 3, − 3 ˆ˜¯ , B ÊÁË 1, 4 ˆ˜¯ , C ÊÁË −1, − 1 ˆ˜¯
A
equilateral
B
obtuse
C
isosceles
D
scalene
9
Name: ______________________
ID: A
Find each measure.
60
m∠1, m∠2, m∠3
A
C
61
B
D
m∠1 = 64, m∠2 = 47, m∠3 = 52
m∠1 = 47, m∠2 = 59, m∠3 = 64
m∠1, m∠2, m∠3
A
C
62
m∠1 = 64, m∠2 = 74, m∠3 = 52
m∠1 = 47, m∠2 = 74, m∠3 = 69
m∠1 = 77, m∠2 = 41, m∠3 = 37
m∠1 = 82, m∠2 = 41, m∠3 = 37
B
D
m∠1 = 77, m∠2 = 36, m∠3 = 30
m∠1 = 82, m∠2 = 92, m∠3 = 30
m∠1, m∠2, m∠3
A
C
m∠1 = 135, m∠2 = 88, m∠3 = 139
m∠1 = 141, m∠2 = 84, m∠3 = 139
B
D
m∠1 = 135, m∠2 = 84, m∠3 = 96
m∠1 = 141, m∠2 = 45, m∠3 = 141
10
Name: ______________________
63
ID: A
m∠1, m∠2, m∠3
A
C
m∠1 = 74, m∠2 = 129, m∠3 = 101
m∠1 = 51, m∠2 = 101, m∠3 = 101
B
D
m∠1 = 46, m∠2 = 129, m∠3 = 129
m∠1 = 74, m∠2 = 152, m∠3 = 74
Name the congruent angles and sides for the pair of congruent triangles.
64
ΔSKL ≅ ΔCFG
A
∠S ≅ ∠G, ∠K ≅ ∠F, ∠L ≅ ∠C, SK ≅ GF, KL ≅ FC, SL ≅ GC
SK ≅ FG, KL ≅ GC, SL ≅ FC
D
65
C
∠S ≅ ∠C, ∠K ≅ ∠F, ∠L ≅ ∠G, SK ≅ CF, KL ≅ FG, SL ≅ CG
∠S ≅ ∠G, ∠K ≅ ∠C, ∠L ≅ ∠F, SK ≅ GC, KL ≅ CF, SL ≅ GF
∠M ≅ ∠T, ∠G ≅ ∠Y, ∠B ≅ ∠W, MG ≅ TY, GB ≅ YW, MB ≅ TW
MG ≅ TW, GB ≅ WY, MB ≅ TY
D
C
68
B
∠M ≅ ∠T, ∠G ≅ ∠W, ∠B ≅ ∠Y,
∠M ≅ ∠W, ∠G ≅ ∠Y, ∠B ≅ ∠T, MG ≅ WY, GB ≅ YT, MB ≅ WT
∠M ≅ ∠Y, ∠G ≅ ∠T, ∠B ≅ ∠W, MG ≅ YT, GB ≅ TW, MB ≅ YW
Refer to the figure. ΔARM, ΔMAX, and ΔXFM
are all isosceles triangles.
67
∠S ≅ ∠F, ∠K ≅ ∠G, ∠L ≅ ∠C,
ΔMGB ≅ ΔWYT
A
66
B
What is m∠RAM?
A 23
B 38
C 42
D
35
What is m∠AMX?
A 80
B 38
C 64
D
72
What is m∠MAX?
A 16
B 38
C 36
D
108
11
69
If m∠FXA = 96, what is m∠FXM?
A 24
B 16
C 12
D 18
70
If m∠FXA = 96, what is m∠XFM?
A 96
B 124
C 132
D 138
71
If m∠FXA = 96, what is m∠FMR?
A 96
B 134
C 152
D 138
72
What is m∠ARM?
A 118
B 114
C 112
D
104
73
If m∠FMR = 155, what is m∠FMX?
A 45
B 55
C 65
D 35
74
If m∠FMX = 23 what is m∠FXA?
A 98
B 95
C 23
D 94
Name: ______________________
75
Triangle FJH is an equilateral triangle. Find x
and y.
A
C
76
77
ID: A
78
Triangle RSU is an equilateral triangle. RT
bisects US. Find x and y.
x=
7
5
, y = 16
B
x = 7, y = 16
A
x=
7
5
, y = 14
D
x = 7, y = 14
x = − 3 , y = 32
C
x=
Triangles ABC and AFD are vertical congruent
equilateral triangles. Find x and y.
A
x = 7, y = 27
C
x=
7
3
, y = 28
B
D
x=
7
3
79
B
D
D
x=
1
2
1
2
, y = 62
, y = 32
, y = 27
x = 7, y = 33
C
80
x = 8, y = 18
x = 4, y = 22
, y = 62
x=
bisects US. Find x and y.
Triangles MNP and OMN are congruent
equilateral triangles. Find x and y.
C
1
3
B
Triangle RSU is an equilateral triangle. RT
A
A
1
x = 4, y = 12
x = 4, y = 6
B
D
x=
x=
5
4
5
4
, y = 12
,y=6
Triangles ABC and AFD are vertical congruent
equilateral triangles. Find x and y.
x = 4, y = 18
x = 8, y = 22
A
C
12
x = 1, y = 5
x = 1, y = 10
B
x = 7, y = 10
x = 7, y = 5
D
Name: ______________________
81
ID: A
84
Triangle RSU is an equilateral triangle. RT
bisects US. Find x and y.
ZC is an altitude, ∠CYW = 9x + 38, and
∠WZC = 17x. Find m∠WZC.
A
85
82
A
x = 3, y = 18
B
x=
12 , y = 42
C
x = 3, y = 42
D
x=
12 , y = 18
34
B
32
C
18
D
31
XW is an angle bisector, ∠YXZ = 7x + 39,
∠WXY = 10x − 13, and ∠XZY = 10x. Find
m∠WZX. Is XW an altitude?
Triangle RSU is an equilateral triangle. RT
bisects US. Find x and y.
A
50; no
B
32; no
C
47; yes
D
17.3; no
Determine the relationship between the
measures of the given angles.
83
A
x=4
5, y=9
C
x=4
5 , y = 21
B
x=4
D
x=4
86
3 , y = 21
∠PTC, ∠VPT
3, y=9
Lines s, t, and u are perpendicular bisectors of
the sides of ΔFGH and meet at J. If
JG = 4x + 3, JH = 2y − 3, JF = 7 and HI = 3z − 4,
find x, y, and z.
A
C
A
C
x = 1, y = 5, z = 5
x = 5, y = 1, z = 5
B
D
x = 2.5, y = 2, z = 2.3
x = 0, y = 6, z = 2.3
13
∠PTC > ∠VPT
∠PTC = ∠VPT
B
∠PTC < ∠VPT
Name: ______________________
87
ID: A
∠JCQ, ∠RCQ
A
C
∠JCQ > ∠RCQ
∠JCQ = ∠RCQ
B
90
An isosceles triangle has a base 9.6 units long.
If the congruent side lengths have measures to
the first decimal place, what is the shortest
possible length of the sides?
A 4.9
B 19.3
C 4.7
D 9.7
91
Which segment is the shortest possible distance
from point D to plane P?
∠JCQ < ∠RCQ
Determine the relationship between the lengths
of the given sides.
88
HB, BL
A
A
HB > BL
determined
89
B
D
HB = BL
C
cannot be
ZX < YX
B
C
ZX > YX
14
DQ
C
DN
D
DR
Find the measure of each interior angle for a
regular pentagon. Round to the nearest tenth if
necessary.
A 360
B 108
C 540
D 72
93
Find the measure of an interior angle of a
regular polygon with 14 sides. Round to the
nearest tenth if necessary.
A 2160
B 25.7
C 154.3
D 360
94
Find the measure of each exterior angle for a
regular nonagon. Round to the nearest tenth if
necessary.
A 1260
B 140
C 360
D 40
95
Find the measure of an exterior angle of a
regular polygon with 20 sides. Round to the
nearest tenth if necessary.
A 360
B 3240
C 162
D 18
HB < BL
ZX = YX
B
92
ZX, YX
A
DP
Name: ______________________
ID: A
Complete the statement about parallelogram ABCD.
96
∠CDA ≅
A ∠ABC; Alternate interior angles are congruent.
B ∠ACD; Alternate interior angles are congruent.
C ∠ABC; Opposite angles of parallelograms are congruent.
D ∠ACD;
Opposite angles of parallelograms are congruent.
97
AD ≅
A
CG; Opposite sides of parallelograms are congruent.
Diagonals of parallelograms bisect each other.
D
C
B
BC;
BC; Opposite sides of parallelograms are congruent.
CG; Diagonals of parallelograms bisect each other.
Refer to parallelogram ABCD to answer to
following questions.
101
Do the diagonals bisect each other? Justify your
answer.
A Yes; AK ≅ CK and DK ≅ BK
B Yes; The
diagonals are not congruent.
and DK ≅ BK
congruent.
102
34 .
of 6
99
B
2
34
C
3
2
D
6
2
What is the distance between points A and C?
A
100
34
34
B
2
34
C
3
2
D
6
2
6
2
What is the length of segment DK?
A
34
B
2
34
C
3
2
D
No; The diagonals are not
2.
B
Yes; Both diagonals have a length
C
Yes; Both diagonals have a
length of 3 2 . D No; The lengths of the
diagonals are not the same.
What is the length of segment AK?
A
No; AK ≅ CK
Are the diagonals congruent? Justify your
answer.
A Yes; Both diagonals have a length of
2
98
D
C
15
Name: ______________________
ID: A
Refer to parallelogram ABCD to answer the
following questions.
Determine whether the quadrilateral is a
parallelogram. Justify your answer.
106
No; Opposite angles are congruent.
Consecutive angles are not congruent.
Consecutive angles are not congruent.
Opposite angles are congruent.
A
103
and DK ≅ BK
congruent.
104
D
No; AK ≅ CK
No; The diagonals are not
What is the length of segment BD?
A
105
D
C
C
Yes;
No;
Yes;
107
Do the diagonals bisect each other? Justify your
answer.
A Yes; AK ≅ CK and DK ≅ BK
B Yes; The
diagonals are not congruent.
B
13
B
13
C
73
D
73
A
Are the diagonals congruent? Justify your
answer.
A Yes; Both diagonals have a length of
73 .
B
C
Yes; Both diagonals have a length of
Yes; Both diagonals have a length of
B
C
D
13 .
Yes; Consecutive angles are not congruent.
No; Consecutive angles are congruent.
No; Opposite angles are not congruent.
Yes; Opposite angles are not congruent.
Determine whether a figure with the given
vertices is a parallelogram. Use the method
indicated.
18.25 .
No; The lengths of the diagonals
are not the same.
D
108
16
A(1, − 6), B(−1, − 3), C(−2, 7), D(0, 4);
Slope Formula
A Yes; The opposite sides have
the same slope. B No; Opposite sides are
the same length. C No;
The opposite sides have the same slope.
D Yes; Opposite sides are the same length.
Name: ______________________
109
ID: A
A(3, − 9), B(10, 1), C(4, 10), D(−9, 3); Distance and Slope Formulas
A No; The opposite sides are not congruent and do not have the same slope.
B Yes;
The opposite sides do not have the same slope. C No; The opposite sides do not have the same slope.
D Yes; The opposite sides are not congruent and do not have the same slope.
Quadrilateral ABCD is a rectangle.
110
If AG = −4k + 24 and DG = 9k + 102, find BD.
A 96
B –6
C 24
D 48
111
If ∠ADB = 2y + 40 and ∠CDB = −3y + 51, find ∠CBD.
A 48
B 1
C 42
D 45
112
In rhombus YZAB, if YZ =12, find AB.
A
113
24
B
12
C
6
D
12
Given each set of vertices, determine whether
parallelogram ABCD is a rhombus, a
rectangle, or a square. List all that apply.
2
In rhombus TUVW, if m∠TUW = 34, find
m∠UVT.
A
56
B
68
C
34
D
114
A(5, 10), B(4, 10), C(4, 9), D(5, 9)
A square; rectangle; rhombus
B rhombus
C square
D rectangle
115
A(−2, 6), B(−2, − 1), C(−9, − 1), D(−9, 6)
A rhombus
B square; rectangle; rhombus
C square
D rectangle
116
For trapezoid JKLM, A and B are midpoints of
the legs. Find ML.
112
A
17
65
B
32.5
C
28
D
3
Name: ______________________
117
For trapezoid JKLM, A and B are midpoints of
the legs. Find ML.
A
118
4
B
34
C
68
D
23
B
8
C
35
D
121
Find five points that satisfy the equation
6 − x = 2y. Graph the points on a coordinate
plane and describe the geometric figure.
122
Find ten points that satisfy the equation
2y < −3x + 1. Graph the points on a coordinate
plane and describe the geometric figure.
Write the inverse of the conditional statement.
Determine whether the inverse is true or false. If
it is false, find a counterexample.
40
For trapezoid JKLM, A and B are midpoints of
the legs. Find AB.
A
119
ID: A
123
The segment bisector is the midpoint.
124
If it is a spider, then it can walk on walls.
125
Two angles measuring 90° are complementary.
126
A conditional statement is formed by a given
hypothesis and conclusion.
127
A line is made up of points.
128
People who live in Texas live in the United
States.
A People who do not live in the United States
do not live in Texas. True B People who do
not live in Texas do not live in the United
States. False; they could live in Oklahoma.
C People who live in the United States live in
Texas. False; they could live in Oklahoma.
D People who do not live in Texas live in the
United States. True
129
All quadrilaterals are four-sided figures.
A All non-quadrilaterals are four-sided figures.
False; a triangle is a non-quadrilateral. B All
four-sided figures are quadrilaterals. True
C No quadrilaterals are not four-sided figures.
True D No four-sided figures are not
quadrilaterals. True
46
For trapezoid ABCD, E and F are midpoints of
the legs. Let GH be the median of ABFE.
Find GH.
A
120
7
B
8
C
4
D
6
Find five points that satisfy the equation
x − 8 = y. Graph the points on a coordinate
plane and describe the geometric figure.
18
Name: ______________________
130
131
132
ID: A
An equilateral triangle has three congruent
sides.
A A non-equilateral triangle has three
congruent sides. False; an isosceles triangle has
two congruent sides. B A figure that has three
non-congruent sides is not an equilateral
triangle. True C A non-equilateral triangle
does not have three congruent sides. True
D A figure with three congruent sides is an
equilateral triangle. True
All country names are capitalized words.
A All capitalized words are country names.
False; the first word in the sentence is
capitalized. B All non-capitalized words are
not country names. True C All non-country
names are capitalized words. False; most of the
words in the sentence are non-capitalized
words. D All non-country names are
non-capitalized words. False; the first word in
the sentence is capitalized.
Independence Day in the United States is July
4.
A July 4 is not Independence Day in the
United States. False; it is Independence Day.
B Non-Independence Day in the United States
is not July 4. True C Non-Independence Day
in the United States is July 4. False; July 4 is
Independence Day in the United States.
D Non-July 4 is not Independence Day in the
United States. True
Write the contrapositive of the conditional
statement. Determine whether the
contrapositive is true or false. If it is false, find
a counterexample.
133
A counterexample invalidates a statement.
134
Vertical angles are two nonadjacent angles
formed by two intersecting lines.
135
If you buy one can of soup, then you get the
second one free.
136
A line is determined by two points.
19
137
Two segments having the same measure are
congruent.
138
If you are 16 years old, then you are a
teenager.
A If you are not a teenager, then you are not
16 years old. True B If you are not 16 years
old, then you are not a teenager. False; you
could be 17 years old. C If you are not a
teenager, then you are 16 years old. True
D If you are a teenager, then you are 16 years
old. False; you could be 17 years old.
139
A converse statement is formed by exchanging
the hypothesis and conclusion of the
conditional.
A A non-converse statement is not formed by
exchanging the hypothesis and conclusion of
the conditional. True B A statement not
formed by exchanging the hypothesis and
conclusion of the conditional is a converse
statement. False; an inverse statement is not
formed by exchanging the hypothesis and
conclusion of the conditional. C A
non-converse statement is formed by
exchanging the hypothesis and conclusion of
the conditional. False; an inverse statement is
formed by negating both the hypothesis and
conclusion of the conditional. D A statement
not formed by exchanging the hypothesis and
conclusion of the conditional is not a converse
statement. True
140
Two angles measuring 180 are supplementary.
A Two angles not measuring 180 are
supplementary. True B More than two angles
measuring 180 are non-supplementary. True
C Non-supplementary angles are not two
angles measuring 180. True
D Non-supplementary angles are two angles
measuring 180. False; supplementary angles
must measure 180.
Name: ______________________
141
142
ID: A
If you have a gerbil, then you are a pet owner.
A If you are not a pet owner, then you do not
have a gerbil. True B If you do not have a
gerbil, then you are not a pet owner. False; you
could have a dog. C If you are not a pet
owner, then you have a gerbil. False; if you are
not a pet owner then you have no pets. D If
you are not a gerbil, then you are not a pet
owner. True
Thanksgiving Day in the United States is
November 25.
A If it is not November 25, it is Thanksgiving
Day in the United States. True B If it is not
Thanksgiving Day in the United States, it is not
November 25. False; Thanksgiving Day could
be another date in a different year so November
25 could be not Thanksgiving Day. C If it is
not November 25, it is not Thanksgiving Day
in the United States. True D If it is not
November 25, it is not Thanksgiving Day in
the United States. False; Thanksgiving Day
could be another date in a different year.
If ZY = 7XY, then ZX = 8XY.
144
Given: FG, MN, HJ, PQ intersect at S;
Write a true conditional statement in if-then
form for the statement, Every equilateral
triangle has three congruent sides.
146
Determine the converse of the conditional
statement, If a triangle is acute, then it has
three acute angles. State whether the converse
is true or false. If the converse is false, find a
counterexample.
147
Write an example of a conditional statement
with its converse.
148
Rain forms when the air in a cloud gets
saturated with water vapors so that it cannot
hold more water vapors. Write a conditional
statement in if-then form for rain.
Write a two-column proof.
143
145
FG⊥HJ.
Prove: If ∠FSM ≅ ∠HSP, then
∠MSH ≅ ∠PSG.
20
149
Write a true conditional statement. Is it
possible to insert the word not into your
conditional statement to make it false? If so,
write the false conditional.
150
Andrew has a made a model as shown. He uses
the concept of noncollinear and noncoplanar
points to find out the number of lines and
planes in the model. How many lines and planes
will he have?
Name: ______________________
151
ID: A
153
A shower stall is formed by a series of
intersecting planes as shown below. Describe
the relationship between the line segments EF
and BG.
ABC ≅ DEF. Using the given vertices,
identify the congruence transformation.
154
A(−1, −4), B(−5, −4), C(−2, 0);
D(−1, 4), E(−5, 4), F(−2, 0)
Identify the congruence transformation from
triangle A to B.
155
152
A(3, 6), B(6, 3), C(4, 2);
D(−3, −6), E(−6, −3), F(−4, −2)
156
A(2, 1), B(3, −4), C(−1, −2);
D(−2, 6), E(−1, −1), F(−5, 3)
Write a two-column proof.
157
21
If BF is a median and a perpendicular bisector
of ΔBDA, then ΔFBA ≅ ΔFBD.
Name: ______________________
ID: A
Write an indirect proof.
158
160
Given: RS is a perpendicular bisector of TV.
Prove: ΔRTV is isosceles
Two sides of a triangle are 3 feet and 4 feet
long. Let x represent the measure of the third
side of the triangle. Suppose x is whole number
such that 2 < x < 5. List the measures of the
sides of the triangles that are possible.
John has five straws. He wishes to use the straws
to make a triangular design. The straws
measure 6 centimeters, 2 centimeters, 7
centimeters, 8 centimeters, and 13 centimeters.
159
Given: ∠ACB ≅ ∠DGF; ∠CAB ≅ ∠GDF
Prove: ∠CBA ≅ ∠GFD
163
Are points A, C, D, and F coplanar? Explain.
161
How many different triangles could John make
with the straws?
162
How many different triangles with even
perimeters could John make?
C
Yes; they all lie on plane P . B No; they are not on the same line.
Yes; they all lie on the same face of the pyramid.
D
No; three lie on the same face of the pyramid and the fourth does not.
A
Complete the truth table.
164
22
Name: ______________________
p
q
r
T
T
T
T
T
F
T
F
T
F
∼q
ID: A
C
r∧ ∼ q
F
F
F
F
A
p
q
r
∼q
r∧ ∼ q
T
T
T
F
F
T
T
F
F
F
T
F
T
T
T
T
F
F
T
F
F
T
T
F
F
F
T
F
F
F
F
F
T
T
T
F
F
F
T
F
p
q
r
∼q
r∧ ∼ q
T
T
T
F
F
T
T
F
F
F
T
F
T
T
T
T
F
F
T
F
F
T
T
F
F
F
T
F
F
T
F
F
T
T
F
F
F
F
T
F
p
q
r
∼q
r∧ ∼ q
T
T
T
F
F
T
T
F
F
F
T
T
T
F
F
T
T
F
T
F
F
F
T
T
T
F
F
F
T
F
F
F
T
T
T
F
F
F
T
F
p
q
r
∼q
r∧ ∼ q
T
T
T
F
F
T
T
F
F
F
T
F
T
T
T
T
F
F
T
F
F
T
T
F
F
F
T
F
F
F
F
F
T
T
F
F
F
F
T
F
D
B
23
Name: ______________________
ID: A
Write the statement in if-then form.
165
A counterexample invalidates a statement.
A If it invalidates the statement, then there is a counterexample.
B If there is a counterexample, then
it invalidates the statement. C If it is true, then there is a counterexample. D If
there is a counterexample, then it is true.
166
Two angles measuring 90 are complementary.
A If two angles measure 90, then two angles measure 90.
B If two angles measure 90, then the angles are
complementary. C If the angles are supplementary, then two angles measure 90. D If the angles are
complementary, then the angles are complementary.
Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false,
find a counterexample.
167
If you have a dog, then you are a pet owner.
A If you are a pet owner, then you have a dog. True
B A dog owner owns a pet. True
C If
you are a pet owner, then you have a dog. False; you could own a hamster. D If you have a dog, then
you are a pet owner. True
168
All Jack Russells are terriers.
A If a dog is a terrier, then it is a Jack Russell. False; it could be a Scottish terrier.
then a dog is a terrier. True C If a dog is a terrier, then a dog is a terrier. True
D All Jack Russells are terriers. True
Refer to the figure below.
169
170
A
BC, AD, HI
D
AB, CD
B
AB, CD, HI
C
CD, HI
24
If it is a Jack Russell,
Name all segments skew to BC.
A
FI, AD, FA, DI
C
CD, AB, BG, CH
FG, GH, HI, FI
B
D
GF, HI, DI, AF
171
Name all planes intersecting plane CHG.
A BAD, CDI, FID, BGF
B CBA, CDI, FIH, BAF
C ADC, DIH, FIH, CHI
D CDA, DAF, FGH, GBA
172
Name all segments skew to GF.
173
Name all segments parallel to GF.
B
A
BC, AD, DI, CH
B
FI, GH, DI, CH
C
AD, AB, BC, CD
D
CD, CH, DI, HI
Name all segments parallel to BG.
A
BA, FG, GH, BC
C
AF, DI, CH
D
B
AD, CD, HI, FI
GH, AD, FI
Name: ______________________
ID: A
174
Name all planes intersecting plane CDI.
A ABC, CBG, ADI, FGH
B CBA, DAF, HGF
C BAD, GFI, CBG, GFA
D DAB, CBG, FAD
175
Name all segments parallel to GH.
176
177
A
BG, CH, FG, HI
C
CD, AB, HI
D
B
179
CD, BA, AF, DI
BC, AD, FI
Name all segments skew to HI.
A
BC, AD, AF, BG
B
FI, GH, DI, CH
C
AD, AB, BC, CD
D
BA, BG, AF, FG
Name all segments parallel to AB.
A
AD, BC, GH, FI
C
CD, FG, HI
D
B
DI, CH, GH, FI
lines c and b¸ f and d¸ c and f¸
c and d¸ b and d B lines a and b¸ a and c¸ a
and d¸ a and f C lines f and d¸ c and f¸
c and d¸ b and d D lines c and b¸ f and d
A
GH, AD, FI
Identify the sets of lines to which the given line
is a transversal.
178
line a
Identify the congruent triangles in the figure.
line j
180
A
lines m and n¸ n and o¸ m and o
lines m
and p¸ n and o C lines i D lines m and n¸ n
and o¸ m and o¸ m and p¸ n and p¸ o and p
A
B
C
ΔKLJ ≅ ΔONM
ΔLJK ≅ ΔOMN
B
ΔSRT ≅ ΔWUV
ΔSTR ≅ ΔWVU
B
D
ΔKJL ≅ ΔOMN
ΔJKL ≅ ΔONM
181
A
C
25
D
ΔRST ≅ ΔWVU
ΔTRS ≅ ΔWUV
Name: ______________________
ID: A
Determine whether ΔPQR ≅ ΔSTU given the coordinates of the vertices. Explain.
182
P ÁÊË 0, 3 ˜ˆ¯ , Q ÁÊË 0, − 1 ˜ˆ¯ , R ÁÊË −2, − 1 ˜ˆ¯ , S ÁÊË 1, 2 ˜ˆ¯ , T ÁÊË 1, − 2 ˜ˆ¯ , U ÁÊË −1, − 2 ˜ˆ¯
No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. B Yes;
Each side of triangle PQR is the same length as the corresponding side of triangle STU. C No; Two sides
of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle
STU. D Yes; Both triangles have an obtuse angle.
A
183
P ÊÁË 3, − 2 ˆ˜¯ , Q ÊÁË 1, 2 ˆ˜¯ , R ÊÁË −1, 4 ˆ˜¯ , S ÊÁË −4, − 3 ˆ˜¯ , T ÊÁË −2, 1 ˆ˜¯ , U ÊÁË 0, 3 ˆ˜¯
Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU. B No;
Each side of triangle PQR is not the same length as the corresponding side of triangle STU. C No; Two
sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of
triangle STU. D Yes; Both triangles have three sides.
A
184
P ÊÁË 4, 0 ˆ˜¯ , Q ÊÁË 2, − 3 ˆ˜¯ , R ÊÁË −1, 4 ˆ˜¯ , S ÊÁË −1, − 4 ˆ˜¯ , T ÊÁË 1, − 1 ˆ˜¯ , U ÊÁË 4, 6 ˆ˜¯
185
Yes; Two sides of triangle PQR and angle PQR are the same measure as the corresponding sides and angle
of triangle STU. B Yes; Each side of triangle PQR is the same length as the corresponding side of triangle
STU. C No; One of the triangles is obtuse. D No; Each side of triangle PQR is not the same length as
the corresponding side of triangle STU.
P ÊÁË −3, 2 ˆ˜¯ , Q ÊÁË −2, − 3 ˆ˜¯ , R ÊÁË −1, 4 ˆ˜¯ , S ÊÁË 2, 4 ˆ˜¯ , T ÊÁË 3, − 1 ˆ˜¯ , U ÊÁË 4, 6 ˆ˜¯
A Yes; Both triangles have three acute angles.
B No; Each side of triangle PQR is not the same length as
the corresponding side of triangle STU. C No; Two sides of triangle PQR and angle PQR are not the same
measure as the corresponding sides and angle of triangle STU. D Yes; Each side of triangle PQR is the
same length as the corresponding side of triangle STU.
A
Identify the type of congruence transformation.
186
A
reflection
B
translation
C
rotation
D
not a congruence transformation
26
Name: ______________________
ID: A
187
A
reflection or translation
B
translation only
C
rotation or translation
D
rotation only
Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.
188
3, 9, 10
A Yes; the third side is the longest.
B No; the sum of the lengths of two sides is not greater than the third.
C No; the first side is not long
enough. D Yes; the sum of the lengths of any two sides is greater than the third.
189
9.2, 14.5, 17.1
A Yes; the third side is the longest.
B No; the first side is not long enough.
C Yes; the sum of the lengths of any two sides is greater than the third.
D No; the sum of the lengths of two sides is not greater than the third.
190
The coordinates of the vertices of a triangle
are A ÊÁË 2, 3 ˆ˜¯ , B ÊÁË 9, 1 ˆ˜¯ , and C ÊÁË 12, 14 ˆ˜¯ . Suppose
193
Samantha’s rectangular gift is 10 inches. by 12
inches and is framed with a ribbon. She wants to
use the same length of ribbon to frame a
circular clock. What is the maximum radius of
the circular clock? Round to the nearest whole
number.
194
Nick framed a square painting that was 30
centimeters long with a decorative strip. He
wants to surround a circular picture frame with
the same length of strip. What is the maximum
radius of the picture frame? Round to the
nearest tenth.
each coordinate is multiplied by 3. What is the
perimeter of this triangle?
191
192
A circular playground of radius 12 feet is
surrounded by chain-link fencing. If the same
length of fencing is used for a square garden,
what is the maximum length of the garden?
Round to the nearest hundredth.
Keith has made a square that has 6-inch cord
sides. He bends the square into a circular loop.
What is the maximum radius of the circular
loop? Round to the nearest tenth.
27
Name: ______________________
195
ID: A
To study types of soil, geologists divide a
surface into smaller geographical cells.
Geologists use computer programs and
laboratory tests to check the suitability of
growing a crop in a region. Explain why
dividing a state into geographical cells allows
geologists to predict crop suitability for that
area.
In the figure below, points A, B, C, and F lie on plane
statement is true.
P . State the postulate that can be used to show each
196
A and B are collinear.
A If two points lie in a plane¸ then the entire line containing those points lies in that plane.
B Through any two points there is exactly one line.
C If two lines intersect¸ then their intersection is exactly one point.
D A line contains at least two points.
197
Line AD contains points A and D.
A If two lines intersect¸ then their intersection is exactly one point.
B If two points lie in a plane¸ then the entire line containing those points lies in that plane.
C A line contains at least two points.
D Through any two points¸ there is exactly one line.
28
Name: ______________________
ID: A
Position and label the triangle on the
coordinate plane.
198
199
one-half equilateral triangle with SU bisecting
the triangle at height a units and base ST 2b
units
right isosceles ΔABC with congruent sides AB
A
and AC a units long
A
B
B
C
C
D
D
29
Name: ______________________
200
ID: A
isosceles ΔFGH with GI twice the length of the
base and bisecting the base
A
B
C
D
30
ID: A
GEOMETRY MIDTERM REVIEW PACKET
Answer Section
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
ANS:
STA:
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STA:
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STA:
C
OBJ: 1-1.1 Identify and model points, lines, and planes.
LA.1112.1.6.1 | MA.912.G.8.1
D
OBJ: 1-1.1 Identify and model points, lines, and planes.
LA.1112.1.6.1 | MA.912.G.8.1
A
OBJ: 1-1.1 Identify and model points, lines, and planes.
LA.1112.1.6.1 | MA.912.G.8.1
B
OBJ: 1-1.1 Identify and model points, lines, and planes.
LA.1112.1.6.1 | MA.912.G.8.1
D
OBJ: 1-1.1 Identify and model points, lines, and planes.
LA.1112.1.6.1 | MA.912.G.8.1
C
OBJ: 1-1.1 Identify and model points, lines, and planes.
LA.1112.1.6.1 | MA.912.G.8.1
C
OBJ: 1-1.4 Identify intersecting lines and planes in space.
LA.1112.1.6.1 | MA.912.G.8.1
A
OBJ: 1-1.4 Identify intersecting lines and planes in space.
LA.1112.1.6.1 | MA.912.G.8.1
D
OBJ: 1-1.4 Identify intersecting lines and planes in space.
LA.1112.1.6.1 | MA.912.G.8.1
B
OBJ: 1-1.4 Identify intersecting lines and planes in space.
LA.1112.1.6.1 | MA.912.G.8.1
D
OBJ: 1-1.4 Identify intersecting lines and planes in space.
LA.1112.1.6.1 | MA.912.G.8.1
C
OBJ: 1-3.1 Find the distance between two points on a number line.
MA.912.G.1.1 | MA.912.G.1.2
D
OBJ: 1-3.1 Find the distance between two points on a number line.
MA.912.G.1.1 | MA.912.G.1.2
B
OBJ: 1-3.2 Find the distance between two points on a coordinate plane.
MA.912.G.1.1 | MA.912.G.1.2
C
OBJ: 1-3.2 Find the distance between two points on a coordinate plane.
MA.912.G.1.1 | MA.912.G.1.2
C
OBJ: 1-3.3 Find the midpoint of a segment.
MA.912.G.1.1 | MA.912.G.1.2
A
OBJ: 1-3.3 Find the midpoint of a segment.
MA.912.G.1.1 | MA.912.G.1.2
B
OBJ: 1-6.1 Identify polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.1 Identify polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
B
OBJ: 1-6.1 Identify polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
1
ID: A
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
ANS:
STA:
ANS:
STA:
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STA:
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STA:
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STA:
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STA:
ANS:
STA:
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STA:
D
OBJ: 1-6.1 Identify polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.1 Identify polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.1 Identify polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
C
OBJ: 1-6.1 Identify polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
C
OBJ: 1-6.1 Identify polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
C
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
B
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
D
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
D
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
C
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
B
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
B
OBJ: 1-6.2 Name polygons.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
B
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
B
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
C
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
B
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
D
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
2
ID: A
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
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STA:
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ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
D
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
D
OBJ: 1-6.3 Find perimeter of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
B
OBJ: 1-6.4 Find circumference of circles.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.4 Find circumference of circles.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.5 Find area of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.5 Find area of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.5 Find area of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.5 Find area of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 1-6.5 Find area of two-dimensional figures.
MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
A
OBJ: 3-2.1 Use the properties of parallel lines to determine congruent angles.
MA.912.G.1.3
A
OBJ: 3-2.1 Use the properties of parallel lines to determine congruent angles.
MA.912.G.1.3
C
OBJ: 3-2.2 Use algebra to find angle measures.
MA.912.G.1.3
D
OBJ: 3-2.2 Use algebra to find angle measures.
MA.912.G.1.3
B
OBJ: 4-1.1 Identify and classify triangles by angles.
MA.912.G.4.1 | MA.912.G.8.6
D
OBJ: 4-1.1 Identify and classify triangles by angles.
MA.912.G.4.1 | MA.912.G.8.6
D
OBJ: 4-1.2 Identify and classify triangles by sides.
MA.912.G.4.1 | MA.912.G.8.6
C
OBJ: 4-2.1 Apply the Angle Sum Theorem.
MA.912.G.2.2 | MA.912.G.8.5 | MA.912.D.6.4 | MA.912.G.8.2
B
OBJ: 4-2.1 Apply the Angle Sum Theorem.
MA.912.G.2.2 | MA.912.G.8.5 | MA.912.D.6.4 | MA.912.G.8.2
C
OBJ: 4-2.2 Apply the Exterior Angle Theorem.
MA.912.G.2.2 | MA.912.G.8.5 | MA.912.D.6.4 | MA.912.G.8.2
A
OBJ: 4-2.2 Apply the Exterior Angle Theorem.
MA.912.G.2.2 | MA.912.G.8.5 | MA.912.D.6.4 | MA.912.G.8.2
C
OBJ: 4-3.1 Name and label corresponding parts of congruent triangles.
MA.912.G.4.4 | MA.912.G.4.6
3
ID: A
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
ANS:
STA:
ANS:
STA:
ANS:
STA:
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ANS:
OBJ:
STA:
C
OBJ: 4-3.1 Name and label corresponding parts of congruent triangles.
MA.912.G.4.4 | MA.912.G.4.6
B
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
D
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
C
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
A
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
C
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
B
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
D
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
A
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
B
OBJ: 4-6.1 Use the properties of isosceles triangles.
LA.910.1.6.5 | MA.912.G.4.1
B
OBJ: 4-6.2 Use the properties of equilateral triangles.
LA.910.1.6.5 | MA.912.G.4.1
A
OBJ: 4-6.2 Use the properties of equilateral triangles.
LA.910.1.6.5 | MA.912.G.4.1
A
OBJ: 4-6.2 Use the properties of equilateral triangles.
LA.910.1.6.5 | MA.912.G.4.1
D
OBJ: 4-6.2 Use the properties of equilateral triangles.
LA.910.1.6.5 | MA.912.G.4.1
C
OBJ: 4-6.2 Use the properties of equilateral triangles.
LA.910.1.6.5 | MA.912.G.4.1
B
OBJ: 4-6.2 Use the properties of equilateral triangles.
LA.910.1.6.5 | MA.912.G.4.1
D
OBJ: 4-6.2 Use the properties of equilateral triangles.
LA.910.1.6.5 | MA.912.G.4.1
D
OBJ: 4-6.2 Use the properties of equilateral triangles.
LA.910.1.6.5 | MA.912.G.4.1
A
OBJ: 5-1.1 Identify and use perpendicular bisectors.
MA.912.G.4.1 | MA.912.G.4.2
A
OBJ: 5-2.1 Use altitudes in triangles.
STA: LA.1112.1.6.1 | MA.912.G.4.2
A
OBJ: 5-2.1 Use altitudes in triangles.
STA: LA.1112.1.6.1 | MA.912.G.4.2
B
5-3.1 Recognize and apply properties of inequalities to the measures of angles of a triangle.
LA.910.1.6.5 | MA.912.G.4.7
4
ID: A
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
ANS: C
OBJ: 5-3.1 Recognize and apply properties of inequalities to the measures of angles of a triangle.
STA: LA.910.1.6.5 | MA.912.G.4.7
ANS: C
OBJ: 5-3.2 Recognize and apply properties of inequalities to the relationships between angles and sides of a
triangle.
STA: LA.910.1.6.5 | MA.912.G.4.7
ANS: C
OBJ: 5-3.2 Recognize and apply properties of inequalities to the relationships between angles and sides of a
triangle.
STA: LA.910.1.6.5 | MA.912.G.4.7
ANS: A
OBJ: 5-5.2 Determine the shortest distance between a point and a line.
STA: LA.1112.1.6.2 | MA.912.G.4.7
ANS: B
OBJ: 5-5.2 Determine the shortest distance between a point and a line.
STA: LA.1112.1.6.2 | MA.912.G.4.7
ANS: B
OBJ: 6-1.1 Find the sum of the measures of the interior angles of a polygon.
STA: MA.912.G.2.2 | MA.912.G.3.4
ANS: C
OBJ: 6-1.1 Find the sum of the measures of the interior angles of a polygon.
STA: MA.912.G.2.2 | MA.912.G.3.4
ANS: D
OBJ: 6-1.2 Find the sum of the measures of the exterior angles of a polygon.
STA: MA.912.G.2.2 | MA.912.G.3.4
ANS: D
OBJ: 6-1.2 Find the sum of the measures of the exterior angles of a polygon.
STA: MA.912.G.2.2 | MA.912.G.3.4
ANS: C
OBJ: 6-2.1 Recognize and apply properties of the sides and angles of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: C
OBJ: 6-2.1 Recognize and apply properties of the sides and angles of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: C
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: D
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: A
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: A
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: D
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: A
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: A
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: D
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
ANS: D
OBJ: 6-3.1 Recognize the conditions that ensure a quadrilateral is a parallelogram.
STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3
5
ID: A
107
108
109
110
111
112
113
114
115
116
117
118
119
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
C
OBJ: 6-3.1 Recognize the conditions that ensure a quadrilateral is a parallelogram.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3
A
OBJ: 6-3.2 Prove that a set of points forms a parallelogram in the coordinate plane.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3
A
OBJ: 6-3.2 Prove that a set of points forms a parallelogram in the coordinate plane.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3
A
OBJ: 6-4.1 Recognize and apply properties of rectangles.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
C
OBJ: 6-4.1 Recognize and apply properties of rectangles.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
B
OBJ: 6-5.1 Recognize and apply properties of rhombi.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
A
OBJ: 6-5.1 Recognize and apply properties of rhombi.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
A
OBJ: 6-5.2 Recognize and apply the properties of squares.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
B
OBJ: 6-5.2 Recognize and apply the properties of squares.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
C
OBJ: 6-6.1 Recognize and apply the properties of trapezoids.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
D
OBJ: 6-6.1 Recognize and apply the properties of trapezoids.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
A
OBJ: 6-6.2 Solve problems involving the medians of trapezoids.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
D
OBJ: 6-6.2 Solve problems involving the medians of trapezoids.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
6
ID: A
120
ANS:
x
1
2
3
−1
−2
y
−7
−6
−5
−9
−10
.
The figure is a straight line.
Substitute the values for x in the given equation and find the corresponding values of y. Plot these points on
a coordinate plane. Join the points and describe the figure formed.
OBJ: 1-1.5 Identify model points, line, planes, collinear points, coplanar points, and intersecting lines and
planes in space.
STA: LA.1112.1.6.1 | MA.912.G.8.1
7
ID: A
121
ANS:
x
2
4
−2
−4
−6
y
2
1
4
5
6
The figure is a straight line.
Substitute the values for x in the given equation and find the corresponding values of y. Plot these points on
a coordinate plane. Join the points and describe the figure formed.
OBJ: 1-1.5 Identify model points, line, planes, collinear points, coplanar points, and intersecting lines and
planes in space.
STA: LA.1112.1.6.1 | MA.912.G.8.1
8
ID: A
122
ANS:
x
1
3
5
0
−2
−3
−4
−5
−6
−6
y
−3
−7
−9
−6
−4
−1
−8
3
−6
6
The figure is a half-plane.
First find the boundary by graphing the related equation 2y = −3x + 1. Then draw a dashed line as the
boundary is not a part of the graph. Test any point to find which half-plane is the solution. For easy
calculation choose ÊÁË 0, 0 ˆ˜¯ .
2y < −3x + 1
0 < 0+1
0 < 1 which is true.
So, the half-plane containing ÊÁË 0, 0 ˆ˜¯ is the solution. Therefore, shade the corresponding half-plane. Look at
the graph and describe the figure.
123
124
125
OBJ: 1-1.5 Identify model points, line, planes, collinear points, coplanar points, and intersecting lines and
planes in space.
STA: LA.1112.1.6.1 | MA.912.G.8.1
ANS:
Sample: The non-segment bisector is not the midpoint. True.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample: If it is not a spider, then it cannot walk on walls. False; it could be a fly.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample: Two angles not measuring 90° are not complementary. True.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
9
ID: A
126
127
128
129
130
131
132
133
134
ANS:
Sample: A nonconditional statement is not formed by a given hypothesis and conclusion. True.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample: A non-line is not made up of points. False; a segment is made up of points and it is not a line.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: B
OBJ: 2-3.3 Write the inverse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: C
OBJ: 2-3.3 Write the inverse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: C
OBJ: 2-3.3 Write the inverse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: D
OBJ: 2-3.3 Write the inverse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: B
OBJ: 2-3.3 Write the inverse of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample: Something that does not invalidate a statement is not a counterexample. True.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample: Two adjacent angles formed by two intersecting lines are not vertical angles. True.
135
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample: If you do not get the second can of soup free, then you do not buy one can of soup. False; you can
buy one without getting the second free.
136
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample: More or fewer than two points do not determine a line. False; many collinear points can determine
a line.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
10
ID: A
137
138
139
140
141
142
143
ANS:
Sample: Noncongruent segments are not two segments having the same measure. True.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: A
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: D
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: C
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: A
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS: C
OBJ: 2-3.4 Write the contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample:
Given: ZY = 7XY
Prove: ZX = 8XY
Proof:
Statements
Reasons
1. ZY = 7XY
1. Given
2. XY = XY
2. Reflexive Property
3. ZX = XY + ZY
3. Segment Addition Postulate
4. ZX = XY + 7XY
4. Substitution Property
5. ZX = 8XY
5. Substitution
OBJ: 2-7.3 Write proofs involving segment addition and congruence.
STA: MA.912.G.8.5
11
ID: A
144
ANS:
Sample:
Given: ∠FSM ≅ ∠HSP; FG⊥HJ
Prove: ∠MSH ≅ ∠PSG
Proof:
Statements
Reasons
1. Given
1. FG, MN, HJ, PQ intersect at S. FG⊥HJ
∠FSM ≅ ∠HSP.
2. ∠HSF, ∠HSG, ∠GSJ, and ∠FSJ are
2. Perpendicular lines intersect to form
right angles.
right angles
3. ∠FSM and ∠MSH are complementary;
3. Complement Theorem
∠HSP and ∠PSG are complementary.
4. m∠FSM + m∠MSH = 90°
4. Definition of complementary
m∠HSP + m∠PSG = 90°
5. m∠FSM + m∠MSH = m∠HSP + m∠PSG 5. Substitution Property
6. m∠FSM = m∠HSP
6. Definition of congruent angles
7. m∠FSM + m∠MSH = m∠FSM + m∠PSG 7. Substitution Property
8. m∠FSM = m∠FSM
8. Reflexive Property
9. m∠MSH = m∠PSG
9. Subtraction Property
10. ∠MSH ≅ ∠PSG
10. Definition of congruent angles
145
OBJ: 2-8.4 Write proofs involving supplementary, complementary, congruent and right angles.
STA: MA.912.G.8.5
ANS:
Sample answer: If a triangle is equilateral, then it has three congruent sides.
The format of if-then form is “If hypothesis, then conclusion.”
146
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample answer: If a triangle has three acute angles, then it is an acute triangle; true.
The converse of a conditional statement ÊÁË p → q ˆ˜¯ exchanges the hypothesis and conclusion of the
conditional. It is also known as q → p.
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
12
ID: A
147
ANS:
Sample answer:
Conditional statement: If a figure is a right triangle, then it has one right angle.
Converse: If a triangle has one right angle, then it is a right triangle.
A conditional statement is a statement that can be written in if-then form. The converse of a conditional
statement ÁÊË p → q ˜ˆ¯ exchanges the hypothesis and conclusion of the conditional. It is also known as q → p.
148
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample answer: If the air in a cloud gets saturated with water vapors, then it rains.
The format of if-then form is “If hypothesis, then conclusion.”
149
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
Sample answer: If there are 366 days in a year, then it is a leap year. Yes; If there are 366 days in a year,
then it is not a leap year.
A conditional statement is a statement that can be written in if-then form. A conditional statement is false
only when the hypothesis is true but the conclusion is false.
150
OBJ: 2-3.5 Analyze and write the converse, inverse and contrapositive of if-then statements.
STA: MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
ANS:
He will have 8 planes and 18 lines.
Points that do not lie on the same line are noncollinear. Points that do not lie in the same plane are
noncoplanar.
151
OBJ: 2-5.3 Identify and use basic postulates about points, lines, and planes. Write paragraph proofs.
STA: MA.912.D.6.4 | MA.912.G.8.1 | MA.912.G.8.5
ANS:
skew lines
Lines that do not intersect and are not coplanar are called skew lines.
152
OBJ: 3-1.3 Identify the relationships between two lines or two planes and name angles formed by a pair of
lines and a transversal.
STA: LA.1112.1.6.1 | MA.912.G.1.3
ANS:
reflection and rotation
OBJ: 4-7.1 Identify reflections, translations, and rotations.
STA: MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
13
ID: A
153
154
155
156
157
ANS:
reflection and translation
OBJ: 4-7.1 Identify reflections, translations, and rotations.
STA: MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
ANS:
reflection
OBJ: 4-7.1 Identify reflections, translations, and rotations.
STA: MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
ANS:
rotation
OBJ: 4-7.1 Identify reflections, translations, and rotations.
STA: MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
ANS:
translation
OBJ: 4-7.1 Identify reflections, translations, and rotations.
STA: MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
ANS:
Sample:
Given: BF is a median and a perpendicular bisector of ΔBDA.
Prove: ΔFBA ≅ ΔFBD
Proof:
Statements
Reasons
1. Given
1. BF is a median and a perpendicular
bisector of ΔBDA.
2. AF ≅ DF
3. ∠BFA, ∠BFD are right angles.
4. ∠BFA ≅∠BFD
5. BF ≅ BF
6. ΔFBA ≅ ΔFBD
OBJ: 5-2.2 Use medians in triangles.
2. Definition of median
3. Definition of perpendicular bisector
4. All right angles are ≅
5. Reflexive Property
6. SAS Theorem
STA: LA.1112.1.6.1 | MA.912.G.4.2
14
ID: A
158
159
ANS:
Sample:
Given: RS is a perpendicular bisector of TV.
Prove: ΔRTV is isosceles
Indirect Proof:
Step 1: Assume ΔRTV is not isosceles, so RT ≠ RV.
Step 2: RS ≅ RS, TS ≅ SV, and ∠RSV ≅ ∠RST. Therefore, by the Hinge Theorem, RT = RV.
Step 3: This contradicts the assumption that RT = RV, so ΔRTV is isosceles.
OBJ: 5-4.3 Use indirect proof with algebra and geometry.
STA: MA.912.D.6.4 | MA.912.G.8.5 | MA.912.G.8.4
ANS:
Sample:
Given: ∠ACB ≅ ∠DGF; ∠CAB ≅ ∠GDF
Prove: ∠CBA ≅ ∠GFD
Indirect Proof:
Step 1: Assume ∠CBA ≠ ∠GFD.
Step 2: m∠ACB + m∠CAB + m∠CBA = 180
m∠DGF + m∠GDF + m∠GFD = 180
m∠ACB + m∠CAB + m∠CBA = m∠DGF + m∠GDF + m∠GFD
If ∠CBA ≠ ∠GFD, then m∠ACB + m∠CAB ≠ m∠DGF + m∠GDF.
Step 3: This contradicts the given information. The assumption must be false, so ∠CBA ≅ ∠GFD.
160
OBJ: 5-4.3 Use indirect proof with algebra and geometry.
STA: MA.912.D.6.4 | MA.912.G.8.5 | MA.912.G.8.4
ANS:
x is either 3 ft or 4 ft; The possible triangles that can be made from sides with those measures are
ÊÁ 3 ft, 4 ft, 3 ft ˆ˜ , ÊÁ 3 ft, 4 ft, 4 ft ˆ˜ .
Ë
¯ Ë
¯
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
161
OBJ: 5-5.3 Apply the Triangle Inequality Theorem and determine the shortest distance between a point
and a line.
STA: LA.1112.1.6.2 | MA.912.G.4.7
ANS:
5
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
OBJ: 5-5.3 Apply the Triangle Inequality Theorem and determine the shortest distance between a point
and a line.
STA: LA.1112.1.6.2 | MA.912.G.4.7
15
ID: A
162
ANS:
1
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. The sum of
the lengths of the possible triangles should be even.
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
OBJ:
and a
ANS:
ANS:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
ANS:
STA:
5-5.3 Apply the Triangle Inequality Theorem and determine the shortest distance between a point
line.
STA: LA.1112.1.6.2 | MA.912.G.4.7
D
OBJ: 1-1.3 Identify coplanar points.
STA: LA.1112.1.6.1 | MA.912.G.8.1
A
OBJ: 2-2.2 Construct truth tables.
STA: MA.912.D.6.1
B
OBJ: 2-3.1 Analyze statements in if-then form.
MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
B
OBJ: 2-3.1 Analyze statements in if-then form.
MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
C
OBJ: 2-3.2 Write the converse of if-then statements.
MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
A
OBJ: 2-3.2 Write the converse of if-then statements.
MA.912.D.6.2 | MA.912.D.6.3 | MA.912.D.6.1
B
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
D
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
B
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
A
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
C
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
A
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
D
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
A
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
C
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
LA.1112.1.6.1 | MA.912.G.1.3
D
OBJ: 3-1.2 Name angles formed by a pair of lines and a transversal.
LA.1112.1.6.1 | MA.912.G.1.3
A
OBJ: 3-1.2 Name angles formed by a pair of lines and a transversal.
LA.1112.1.6.1 | MA.912.G.1.3
C
OBJ: 4-3.2 Identify congruent transformations.
MA.912.G.4.4 | MA.912.G.4.6
D
OBJ: 4-3.2 Identify congruent transformations.
MA.912.G.4.4 | MA.912.G.4.6
16
ID: A
182
183
184
185
186
187
188
189
190
ANS: B
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
STA: MA.912.G.4.6 | MA.912.G.4.8
ANS: A
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
STA: MA.912.G.4.6 | MA.912.G.4.8
ANS: D
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
STA: MA.912.G.4.6 | MA.912.G.4.8
ANS: D
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
STA: MA.912.G.4.6 | MA.912.G.4.8
ANS: B
OBJ: 4-7.1 Identify reflections, translations, and rotations.
STA: MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
ANS: B
OBJ: 4-7.1 Identify reflections, translations, and rotations.
STA: MA.912.G.2.4 | MA.912.G.2.6 | MA.912.G.4.3
ANS: D
OBJ: 5-5.1 Apply the Triangle Inequality Theorem.
STA: LA.1112.1.6.2 | MA.912.G.4.7
ANS: C
OBJ: 5-5.1 Apply the Triangle Inequality Theorem.
STA: LA.1112.1.6.2 | MA.912.G.4.7
ANS:
about 106.5
Use the distance formula, d =
ÊÁ x − x ˆ˜ 2 + ÊÁ y − y ˆ˜ 2 to calculate the length of the sides. Then add these
ÁË 2
ÁË 2
1˜
1˜
¯
¯
lengths to find the perimeter.
191
OBJ: 1-6.6 Identify and use special pairs of angles and polygons, find the perimeter and area of
two-dimensional figures and find the circumference of circles.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
ANS:
18.85 ft
Here, the circumference of the circular playground is equal to the perimeter of the square garden. Use this
relationship to find the maximum length of the garden
192
OBJ: 1-6.6 Identify and use special pairs of angles and polygons, find the perimeter and area of
two-dimensional figures and find the circumference of circles.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
ANS:
3.8 in.
Here, the perimeter of the square is equal to the circumference of the circular loop. Use this relationship to
find the maximum radius of the loop.
OBJ: 1-6.6 Identify and use special pairs of angles and polygons, find the perimeter and area of
two-dimensional figures and find the circumference of circles.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
17
ID: A
193
ANS:
7 in.
Here, the perimeter of the rectangular gift pack is equal to the circumference of the circular clock. Use this
relationship to find the maximum radius of the clock.
194
OBJ: 1-6.6 Identify and use special pairs of angles and polygons, find the perimeter and area of
two-dimensional figures and find the circumference of circles.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
ANS:
19.1 cm
Here, the perimeter of the square painting is equal to the circumference of the circular picture frame. Use
this relationship to find the maximum radius of the frame.
OBJ: 1-6.6 Identify and use special pairs of angles and polygons, find the perimeter and area of
two-dimensional figures and find the circumference of circles.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
18
ID: A
195
ANS:
Crop suitability is more predictable for a smaller area.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
196
197
198
199
OBJ: 1-6.6 Identify and use special pairs of angles and polygons, find the perimeter and area of
two-dimensional figures and find the circumference of circles.
STA: MA.912.G.2.5 | MA.912.G.2.6 | MA.912.G.2.1 | MA.912.G.2.7
ANS: B
OBJ: 2-5.1 Identify and use basic postulates about points, lines, and planes.
STA: MA.912.D.6.4 | MA.912.G.8.1 | MA.912.G.8.5
ANS: C
OBJ: 2-5.1 Identify and use basic postulates about points, lines, and planes.
STA: MA.912.D.6.4 | MA.912.G.8.1 | MA.912.G.8.5
ANS: B
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
ANS: C
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
19
ID: A
200
ANS: C
OBJ: 4-8.1 Position and label triangles for use in coordinate proofs.
STA: MA.912.D.6.4 | MA.912.G.4.8 | MA.912.G.8.5
20