Download GEO SEM 1 REVIEW

Lincoln Public Schools
Geometry
REVIEW
Semester One
CALCULATOR
Revised 12/2007
1.
Describe the lines in the sketch.
A. coplanar and intersecting
B. coplanar and nonintersecting
C. noncoplanar and intersecting
D. noncoplanar and nonintersecting
2.
If mABC = 100°, find m ABD .
A. 60°
B. 70°
●D
●
A
C. 80°
D. 90°
3.
●
B
30°
●
C
SU is the bisector of RST . Find mRST and mRSU .
A. mRST = 52°, mRSU = 26°
R●
B. mRST = 90°, mRSU = 38°
U●
C. mRST = 104°, mRSU = 52°
●
D. mRST = 114°, mRSU = 52°
4.
52°
S
Which answer best describes how 1 and 3 are related?
A. complementary angles
B. linear pair of angles
1
3
C. supplementary angles
D. vertical angles
5.
A and B are supplementary angles. If m B = 36°, find m A .
A.
54°
B.
72°
C. 144°
D. 180°
●
T
6.
m1 = 72°. Find m2 .
A.
M●
8°
B. 18°
C. 28°
D. 72°
7.
●
P
1
O
2
●
N
Write as a biconditional statement: “If two lines are perpendicular, then they
meet to form right angles.”
A. Two lines are perpendicular if and only if they meet to form right angles.
B. Two lines are perpendicular if they meet to form right angles.
C. If two lines meet to form right angles, then they are perpendicular.
D. If two lines are perpendicular, then they meet to form right angles.
9.
Conditional Statement: “If the traffic light is green, then you may
cross the street.” Which statement represents the inverse.
A. If you cannot cross the street, then the traffic light must not be green.
B. If the traffic light is not green, then you may not cross the street.
C. If you cross the street, then the traffic light must be green.
D. The traffic light must be green if you cross the street.
10.
Identify the property used to complete the statement:
If 3x − 4 = 14, then 3x = 18.
A. Addition Property of Equality
B. Division Property of Equality
C. Multiplication Property of Equality
D. Subtraction Property of Equality
11. How many lines through point Q are parallel to line m?
A. zero
●Q
B. one
C. two
D. infinitely many
12.
m
What type of angles are 1 and 5 ?
A. alternate exterior
B. alternate interior
1
3
C. consecutive interior
2
4
9
10
11
12
D. corresponding
6
5
7
13.
Name a line skew to AB .
A. CD
H
G
B
A
F
E
B. BH
C. GH
8
C
D
D. CE
14.
Which pair of angles are alternate exterior angles?
A. 1 and 5
B. 1 and 8
C. 2 and  4
D. 3 and 6
2
1
4
6
8
3
5
7
13
14
15
16
15.
Name a pair of lines that must be parallel and state the reason for your
conclusion.
p
q
A. p and q; corresponding angles are congruent.
B. p and q; alternate interior angles are congruent.
l
C. l and m; corresponding angles are congruent.
D. l and m; alternate exterior angles are congruent.
16.
m
Find the measure of 1 .
1
A. 38°
B. 42°
C. 52°
D. 68°
38°
17.
Solve for x.
A.
65°
B.
85°
110°
100°
65°
x
C. 110°
D. 115°
18.
Parallelogram ABCD and parallelogram WXYZ are congruent. Find the
value of m.
B
A. 3.3
C
(3m + 70)°
X (10m)°
80°
B. 8
C. 8.5
D. 10
A
D
W
Z
Y
19.
What theorem or postulate is used to prove the two triangles are congruent?
A. AAA
B. AAS
C. SAS
D. SSS
20.
Find the value of x.
A.
50°
B.
80°
x
C. 100°
D. 130°
130°
21.
E
Find the measure of x.
x
A. 15°
B. 30°
B
C. 45°
D. 60°
C
22.
D
What is the length of AP?
A.
6
B.
7
C.
8
A
6
B
D. 10
P
C
8
23.
Find BC.
A
A.
3.2
B.
6.4
B
C. 12.8
D. 25.2
24.
C
D
E
12.8
Which of the following could be the length of ST ?
T
A. 20
B. 27
12
C. 28
D. 30
25.
S
R
15
List the angles from smallest to largest.
A. A , B, C
B
B. B , C,A
10
11
C. C , A, B
D. C , B, A
26.
A
C
12
List the sides of the triangle from shortest to longest.
B
A. AB, AC, BC
B. AC, AB, BC
C. AB, BC, AC
D. BC, AC, AB
A
70°
50°
C
27.
Find the value of x.
A.
8
B.
9
C. 17
(8x + 10)°
(7x + 4)°
(2x + 6)°
D. 19
(3x)°
28.
Find the value of x.
A.
2
B.
6
C.
8
x+2
D. 10
29.
8
If ABCD is a parallelogram, then what are the coordinates of the
midpoint of BD ?
A. (8, 4)
A (2, 4)
B
B. (4, 2)
C. (3, 0)
D. (1, 2)
30.
C (6, 0)
D
If QRST is a parallelogram, then what is the mQ ?
A. 290°
S
R
B. 110°
C. 70°
D. 20°
70°
Q
T
31.
If KLMN is a square, then what is the mLPM ?
K
A. 30°
L
B. 45°
C. 60°
P
D. 90°
N
32.
M
Solve for x.
x
A. 10
20
B. 15
C. 20
25
D. 25
33.
Identify the polygon.
A. kite
110°
110°
B. parallelogram
C. rhombus
70°
D. trapezoid
34.
Find the area of DEF .
E
A. 10 square units
B. 25 square units
5
C. 30 square units
D. 50 square units
D
2
10
F
G
35.
Find the area of the trapezoid.
A.
48 square units
B.
60 square units
A
9
8
B
7
6
C. 120 square units
D. 320 square units
36.
D
C
12
Find the area of the kite.
5
5
A. 22 square units
B. 32 square units
C. 44 square units
4
4
8
D. 64 square units
37.
What is the converse of the statement “If I live in Lincoln, then I live in
Nebraska”?
A. If I do not live in Lincoln, then I do not live in Nebraska.
B. If I do not live in Lincoln, then I live in Nebraska.
C. If I live in Nebraska, then I do not live in Lincoln.
D. If I live in Nebraska, then I live in Lincoln.
38.
Find the distance between the points (3,9) and (-1,2).
A.
11
B.
53
C.
65
D.
121
39.
If JK = KL, L is the midpoint of JM , and KL = 6, then what is the measure
of KM ?
A. 3
B. 6
J
●
K
●
L
M
C. 12
D. 18
40.
Choose the property being illustrated: AB = AB.
A. Distributive Property of Equality
B. Reflexive Property of Equality
C. Symmetric Property of Equality
D. Transitive Property of Equality
41.
Use the diagram to determine which statement is true.
A. Points W, T, and V are collinear.
R● ● U
●
T
●
S
B. TU is perpendicular to line a.
C. UTV and STW are vertical angles.
●W
D. RTU and UTV are complementary.
b
42.
Given the figure with m NKL = 120°, find m JKM .
A. 25°
B. 35°
●
P
C. 100°
D. 110°
●
J
●N
25°
●M
50°
●
K
●
L
●
V
a
43.
Which would be the correct statement for step 2 in the proof?
STATEMENTS
REASONS
1. 1 and 2 are vertical angles
1. Given
2. ___________________
2. Vertical Angles Theorem
A. 1 and 2 are complementary.
B. 1 and 2 are congruent.
C. 1 and 2 are supplementary.
D. 1 and 2 are a linear pair.
44.
Find m  4 and m  7.
1
A. m  4 = 105°, m  7 = 105°
3
B. m  4 = 105°, m  7 = 75°
C. m  4 = 75°, m  7 = 105°
SV bisects RST . Find m VST .
A.
7°
B. 14°
●
R
●V
(2x + 19)°
C. 33°
●
S
D. 66°
46.
4
5 6
7 105°
D. m  4 = 75°, m  7 = 75°
45.
2
(10x – 37)°
●
T
Find the value of a.
A. 13.3
B. 15
C. 31.3
D. 40
(2a + 10)°
(4a – 20)°
47.
If  1 and  2 are complementary and  2 and  3 are complementary, what
is always true about  1 and  3?
A. They are complementary.
B. They are congruent.
C. They are supplementary.
D. They are vertical angles.
48.
Which can be used to show x // y?
y
x
60°
60°
z
A. If two lines are cut by a transversal so that alternate interior angles are
congruent, then the lines are parallel.
B. If two lines are cut by a transversal so that alternate exterior angles are
congruent, then the lines are parallel.
C. If two lines are cut by a transversal so that consecutive interior angles are
congruent, then the lines are parallel.
D. If two lines are cut by a transversal so that corresponding angles are
congruent, then the lines are parallel.
49.
Find the value of x.
A. 50
B. 70
(2x – 40)°
(x + 10)°
C. 100
D. 150
50.
Find counterexample to show the following conditional statement is false.
“If a number is prime, then it is odd.”
A. 1
B. 2
C. 5
D. 6
51.
Given A(8,-10) and B(6,-2), find the midpoint of AB.
A. (-6,7)
B. (1,-4)
C. (7,-6)
D. (14,-12)
52.
If two angles form a linear pair, then the angles are supplementary.  X and
 Y form a linear pair. Which conclusion represents a proper application of the
Law of Detachment to these statements?
A.  X and  Y are vertical angles.
B.  X and  Y have the same measure.
C.  X and  Y are complementary.
D.  X and  Y are supplementary.
53.
Find the value of x.
(2x + 10)°
A. 4
B. 6
C. 18
(4x + 2)°
D. 32
54.
Classify the triangle according to its angles.
A. acute
B. equiangular
C. obtuse
D. right
55.
Classify the triangle according to its sides.
A. equilateral
B. right
C. scalene
60°
60°
56.
Which statement is true of all rectangles?
A. Diagonals are congruent.
B. Diagonals are perpendicular.
C. Consecutive sides are congruent.
D. They are equiangular and equilateral.
57.
Name a pair of congruent parts using corresponding parts of congruent
triangles are congruent.
B
A. ABC  ADC
B. ABC  CDA
A
C
C. AB  DA
D. DC  AC
58.
D
Which of the following is always a parallelogram with perpendicular diagonals?
A. isosceles trapezoid
B. rectangle
C. rhombus
D. trapezoid
59.
 DEF is an obtuse isosceles triangle. Identify the relationship between
angles D and F.
A.  D and  F are complementary angles.
D
B.  D and  F have the same measure.
C.  D and  F are a linear pair.
110°
E
D.  D and  F are supplementary angles.
60.
Find the measure of x.
A.
52°
B.
64°
x
C. 104°
D. 128°
52°
F
61.
Find the area of the shaded region.
A. 24 sq. units
6
6
6
6
B. 48 sq. units
C. 96 sq. units
D. 120 sq. units
8
62.
Which statement would best complete the proof?
B
Given: B  E , BC  EC
A
Prove: ED  BA
C
STATEMENTS
1. B  E
REASONS
1. Given
2. BC  EC
3. ACB  DCE
4. ACB  DCE
2. Given
3. Vertical Angles Theorem
4. ASA Congruence Postulate
5. ED  BA
5.
D
E
A. Angle, Side, Angle
B. Corresponding Parts of Congruent Triangles are Congruent
C. Side, Angle, Side
D. Side, Side, Side
63.
If m  4 = 110°, then which statement must be true?
A. m  1 = 110°
1
B. m  2 = 110°
C. m  1 > 110°
D. m  2 < 110°
2
3
4
64.
Which segment is longest?
A.
B.
C.
D.
S
PQ
PS
SQ
PQ
P
20°
28°
68°
R
Q
65.
The area of  XYZ is 60 in 2 and XY= 10 in. Find ZW.
Z
A. 3 in
B. 6 in
C. 12 in
D. 24 in
X
66.
Y
W
Find m  1.
54°
A. 112°
67.
B.
70°
C.
68°
D.
54°
1
124°
Given m  RSV = m  VST, RW = WT, and SU  RT . Name a median.
S
A. SU
B. SW
C. RV
D. RW
R
U
V
W
T
Use the diagram for #68 - 72.
68.
69.
Name three collinear points.
A.
W, S, V
B.
W, V, P
C.
R, S, P
D.
R, S, V
What is another name for line y?
A. P
B. W
C. PT
D. PV
70.
Name two opposite rays.
A. SR and SV
B. SR and SW
C. ST and SV
D. ST and SR
71.
Name two vertical angles.
A. RSW and PSV
B. RSW and WSV
C. RSP and RSV
D. RSP and PSW
72. Name one linear pair of angles.
A. RSW and PSV
B. RSW and WSV
C. RSP and RSV
D. RSP and PSW
R
●
W
●
●
S
T
●
P
●
y
V
●
x
77.
Which best describes the polygon?
A. equiangular
B. equilateral
C. regular
78.
Which best describes the polygon?
A. concave, heptagon
B. concave, regular
C. convex, heptagon
D. convex, regular
OPEN-ENDED
79.
The perimeter of rectangle ABCD is 78m. Find the value of x, the length of BC ,
and the area of ABCD.
B
C
15 m
A
80.
(3x + 6) m
D
68. x=
BC =
Area =
a) Sketch, with appropriate markings, one acute triangle, one right triangle and
one obtuse triangle. Then sketch all three angle bisectors for each triangle.
b) True or False: The angle bisectors of a triangle always meet inside the
triangle.
81.
a) Sketch, with appropriate markings, one acute triangle, one right triangle and
one obtuse triangle. Then sketch all three medians for each triangle.
b) True or False: The medians of a triangle always meet inside the triangle.
83.
C is the centroid of  GHJ and CM = 8. Find CH and HM.
H
5. CH =
HM =
C●
G
84.
J
M
Given: VW , WX , and XV are midsegments of  RST, VW = 12, WX = 7, and
ST = 20.
Find: VX and the perimeter of  RST.
S
6. VX =
V
12
W
perimeter =
7
R
X
T
85.
Given: JKLM is a parallelogram, JN = (2x – 1) and NL = (x + 10).
Find: x, JN and JL.
J
K
7. x =
(2x − 1)
N
(x + 10)
JN=
86.
Use the diagram to find each.
1
4
5
8
88.
JL=
L
M
2
3
6
7
a) one pair of alternate exterior angles
a)
b) one pair of alternate interior angles
b)
c) one pair of consecutive interior angles
c)
d) one pair of corresponding angles
d)
Use the diagram, where RST  XYZ , to find the missing measures.
S
Y
9
R
mS =
mT =
110°
mX =
12
4
mY =
45°
T
Z
X
XZ =
XY =
YZ =
Matching. Match the description to the appropriate diagram. You may use some
diagrams more than once.
89.
scalene right triangle
90.
isosceles right triangle
91.
scalene triangle
92.
isosceles triangle
93.
complementary base angles,  1,  2
94.
congruent base angles,  1,  2
95.
supplementary angles,  1,  2
96.
complementary angles,  1,  2
1 2
A.
B.
1
C.
D.
2
1
2
1
2
E.
8
6
3
F.
5
4
3
# 97 – 102, Decide whether enough information is given to prove that the
triangles are congruent. If there is enough information, state the congruence
postulate you would use.
97.
98.
99.
100.
101.
102.
#103-105, Decide whether the figure is a polygon. If it is, then use the number of
sides to state what kind of polygon it is.
103.
104.
105.
#106-107, Describe the pattern and predict the next number.
106.
20, 18, 15, 11…
pattern:
next number:
107.
3,6,12,24,…
pattern:
next number: