Download Geometry Semester Review Packet

Geometry
Semester Review Packet
True or False.
1.
Two lines always lie in the same plane.
2.
There are lines which do not intersect each other.
3.
If three points are collinear, then they are coplanar.
4.
Any two points are collinear.
5.
A line has two endpoints.
6.
Given two points, there is more than one plane containing them.
7.
If two complementary angles are congruent, then each is a right angle.
8.
If AB and CD intersect at O, then mAOC = mBOD.
9.
If mQ = 100, then Q does not have a complement.
10.
If two angles have the same measure, then they are vertical angles.
11.
Vertical angles are never supplementary.
12.
The bisector of the vertex angle of an isosceles triangle bisects the base and is  to the base.
13.
The base angles of an isosceles triangle are acute.
14.
An altitude of a triangle lies in the interior of the triangle.
15.
If the three angles of a triangle have unequal measures, then no two sides of the triangle are
congruent.
16.
Two lines which are perpendicular to a third line are parallel.
17.
Every right triangle has two acute angles.
18.
The longest side of any triangle is called the hypotenuse.
19.
The median of a triangle bisects the side to which it is drawn.
20.
Each side of an angle is a ray.
21.
The diagonals of a square are perpendicular to each other.
22.
A square is a parallelogram.
23.
If two consecutive angles of a quadrilateral are right angles, then the quadrilateral is a
parallelogram.
24.
If a diagonal of a parallelogram divides it into two isosceles triangles, the parallelogram
is a rhombus.
25.
If each pair of opposite sides of a quadrilateral are congruent, then the quadrilateral
is a parallelogram.
26.
Opposite angles of a parallelogram are congruent.
27.
If the diagonals of a quadrilateral are perpendicular and congruent, then the quadrilateral
is a square.
28.
A diagonal of a parallelogram bisects two of its angles.
29.
A quadrilateral with three right angles is a rectangle.
30.
If a quadrilateral has a pair of opposite sides parallel and a pair of opposite sides congruent,
then the quadrilateral is a parallelogram.
Always, Sometimes or Never True
31.
An equilateral triangle is isosceles.
32.
An angle has a complement.
33.
A ray has two endpoints.
34.
An angle is equal to its supplement.
35.
A right triangle is isosceles.
36.
The complement of an acute angle is an obtuse angle.
37.
Two lines perpendicular to a third line are skew.
38.
Two skew lines are coplanar.
39.
If two angles have a common side, the angles are adjacent.
40.
The supplement of an obtuse angle is an obtuse angle.
41.
Complementary angles are congruent to each other.
42.
A ray has a midpoint.
43.
Supplementary angles are adjacent.
44.
Congruent angles are supplementary.
45.
Theorems are reversible.
46.
Three parallel lines are coplanar.
47.
A square is a rectangle.
48.
If the diagonals of a quadrilateral are perpendicular, then the quadrilateral is a rhombus.
49.
The diagonals of a rectangle bisect each other.
50.
A trapezoid with three congruent sides is isosceles.
Problems
51.
One of two supplementary angles is 8 more than the other.
Find the measure of the larger angle.
52.
Two consecutive angles of a parallelogram are in the ratio 7:5.
Find the measure of the smaller angle.
53.
The measures of the base angles of an isosceles triangle are 3x+5 and 5x25 and the
measure of the vertex angle is 6x10. Find the measure of each angle.
54.
Find the slope of the line through (5, 1) and (2, 7).
55.
A line passes through (9, y) and (2, 6) and has slope
56.
The vertices of RKC are R(8, 2), K(3, 9) and C(0, 4). Find the slope of the line
through C that is parallel to RK .
57.
The vertices of ATM are A(3, 1), T(1, 5) and M(1, 2). Find the slope of the altitude
from T to AM .
58.
What are the restrictions on the value of
x in the figure at the right?
x
9
. Find the value of y.
2
38
P
59.
Given PM  QT , PQ  PT , mQ  3x 11 and mPMT  4 x  6 ,
find mQPT.
Q
60.
M
T
Find the area of a circle whose center is at the origin that passes through the point (7, 0).
(Round to the nearest hundredth)
61.
F

Given FT  EY , FE = 5x + 7, TY = 3x + 41
and TE = 5, find FT.
T

E

Y

a
62.
Is a  b? Show why!
63.
In the figure, a  b.
(3x  18)
a) If m7 = 100, find m3.
1
2
a
b) If m7 = 96, find m6.
(x + 58)
b
8
7
c) If m1 = 120, find m5.
3
d) If m4 = 20, find m7.
b
4
6
5
e) If m4 = 30, find m1.
f) If m5 = 117, find m7.
64.
Given AO  BO and AZ  BZ , what conclusion can
A
be made about OZ ? Why?
O
Z
B
B
65.
In the diagram,
37
a) Find mADC
A
60
35
b) Find mABC
C
61
D
66.
116
Find mA.
A
41
67.
MTH is equilateral with MT = x + 8, TH = 2x  3 and MH = 3x  14.
Find the perimeter of MTH.
68.
If BD is an altitude of ABC, what conclusion must be true? Why?
A
D
B
a
69.
If a  b, find mNOT.
b
N
O
T
(3x  18)
(2x + 24)
S
70.
Given RS  CD and CD bisects SCM, find mSCR.
D
56
R
71.
C
M
The ratio of the measure of 1:2 is 1:4. Find m2.
2
1
72.
If AOC  DOB, what conclusion must be true? Why?
B
A
C
O
D
C
For each of the following, determine if the triangles can be proved congruent. If they can be
proved congruent, give the reason (SSS, SAS, ASA, or HL). Otherwise, write NONE.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
Multiple Choice
85.
Which of the following statements are always reversible.
a) postulates
86.
b) theorems
c) definitions
d) a & b
Points M, P and O are collinear. If MO = 8, PO = 12 and MP = 4 then _?_
a) P lies between M and O
c) M lies between P and O
b) O lies between M and P
d) none of these
e) b & c
87.
What can you assume from the diagram?
a) EBC is a right angle
D
E
b) points E, F and B are collinear
F
c) EFB is a straight angle
d) CB  DE
C
B
A
e) b & c
88.
In the figure for #87, CD  CB = _?_
b) DCB
a) point C
89.
b) A  C
b) 60
Subtract:
b) 45
d) none of these
c) 32
d) 30
e) none of these
c) 144
d) 64
e) none of these
90  3917’42”
a) 5043’18”
93.
c) B  C
The ratio of the measures of 1 and 2 is 4:1. If 1 and2 form a straight angle find m1.
a) 36
92.
e) none of these
The supplement of an angle is four times the complement. Find the measure of the angle.
a) 120
91.
d) CB
If A is supplementary to B and C is supplementary to B, then _?_
a) A  B
90.
c) ABD
b) 5042’17”
c) 5142’18”
d) 5042’18”
Given BA  BC , find mDBC.
A
a) 15b) 19
c) 28
e) none of these
D
3x+5
d) 64
2x10
B
C
A
94.
Given: AE is the  bisector of FC , mF = 4x+30,
mC = 2y+40, AF = y+5, AC = 3y5
Find mF
95.
96.
a) 34
b) 50
c) 30
d) 26
F
E
C
2 and 5 are vertical angles. If m2 = 4x 18 and m5 = 2x + 26, find the value of x.
a) 4
b) 14
c) 22
d) 44
If a  b, name a pair of angles that are “not” congruent.
1
a
3
a) 1 and 2
b) 2 and 3
4
c) 3 and 4
97.
b
2
d) 1 and 3
ABC is isosceles with base AC . If mA = x+14, mB = 7x1 and mC = 2x3. Find mB.
a) 17
b) 31
c) 63
d) 118
e) none of these
G
Using the figure at the right, give the reason
for each of the following.
98.
a) multiplication
d) defn midpoint
99.
b) division
e) cannot be proved
C
B
D
c) subtraction
Given: CGD  FGE
Conclusion: CGE  FGD
a) addition
d) multiplication
100.
A
Given: A and B are midpoints, AG  BG
Conclusion: CG  FG
b) subtraction
e) cannot be proved
c) substitution
b) addition
e) cannot be proved
c) substitution
Given: CG  GF
Conclusion: AC  BF
a) multiplication
d) subtraction
E
F
101.
A box contains five triangles, One is scalene, one is isosceles, two are equilateral and
one is equiangular. If one triangle is selected at random, what is the probability that
the triangle is isosceles?
a)
1
5
b)
2
5
c)
3
5
d)
4
5
e) none of these
A
102.
In the figure, AC  AD , B and E are midpoints.
Which triangles can be proved congruent?
a) ABD  AEC
b) BCD  EDC
c) BPC  EPD
d) a & b
B
e) none of these
103.
C
D
The methods for proving that two lines are perpendicular are _?_
a)
b)
c)
d)
e)
104.
E
P
two lines that form congruent adjacent angles
two lines intersect to from right angles
one line is the perpendicular bisector of the other
a, b & c
b&c
In the figure, BD  bisector of AC , AB = 5x+4,
BC = 7x8 and AC = 3x+6. Find AD.
A
D
a) 6
b) 12
c) 24
d) none of these
B
C
a
105.
If 2  6, which lines must be parallel?
c
6
2
a) a and b
c) none of these
b) c and d
d
b
106.
If ab, find m1.
a
b
a) 50b) 110
(x + 20)
c) 70
(2x + 10)
1
d) 150
e) none of these
107.
In the figure, BX bisects ABC
Find m1.
A
X
a) 25b) 30
c) 20
1
2
d) 50
B
108.
In a parallelogram, opposite angles are _?_
a) supplementary
109.
110.
111.
115
C
b) complementary
c) congruent
d) acute
The diagonals of a rhombus _?_
a) bisect opposite angles
b) are congruent
d) b & c
e) a & c
c) are perpendicular
In an isosceles trapezoid, the _?_
a) diagonals are congruent,
b) opposite angles are supplementary
c) legs are congruent
d) a, b & c
If the diagonals of a quadrilateral bisect each other and are perpendicular, then the
quadrilateral is a _?_
a) rectangle
b) rhombus
c) square
d) trapezoid
D
112.
113.
If ABCD is a parallelogram, which of the following must be true?
a) C  D
b) A  C
c) mB + mD = 180
d) AB  BC
If LUCK is a square, which of the following is NOT necessarily true.
a) mLKU = 45
b) mKCU = 90
c) LU = UC
d) LC  KU
e) all are true
114.
Which of the following is not a property of an isosceles trapezoid?
a) base angles are congruent
b) opposite angles are supplementary
c) legs are congruent
d) diagonals are congruent
e) all are properties of an isosceles trapezoid
Problems
115.
FGHJ is a parallelogram, FG = x+5, GH = 2x+3
mG = 40, mJ = 4x+12
F
J
a) Find mF
b) Find the perimeter of FGHJ
G
H
S
116.
N
SNOW is a square with mSON = 2x + 3 and YW = x  9.
Find SO.
Y
W
O
Prove each of the following.
C
B
F
117.
Given:
Prove:
ABCD is a parallelogram: AF  CE
DF  BE
E
D
A
A
118.
Given:
oO, AOB  AOC
Prove:
B  C
O
B
C
A
119.
Given:
Prove:
AB  CD : AB bisects CAD
ACD is isosceles
C
B
D
T
120.
Given:
KOT is isosceles with base KT
OPM  T
Prove:
PM  KT
M
O
P
K
Geometry
Answers to First Semester Review Packet
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
False
True
True
True
False
True
False
True
True
False
False
True
True
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
Always
Sometimes
Never
Sometimes
Sometimes
Never
Sometimes
Never
Sometimes
Never
Sometimes
Never
Sometimes
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
False
True
False
True
False
True
True
True
True
False
True
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
Sometimes
Sometimes
Sometimes
Always
Sometimes
Always
Always
94
75
50, 50, 80
8
3
37.5
7
11
4
3
38 < x < 180
58
 153.93
87
25. True
26. True
27. False
28. False
29. True
30. False
54.
55.
56.
57.
58.
59.
60.
61.
62. No; lines do not form right angles
63. a) 100
b) 84
c) 120
d) 160
e) 150
f) 117
64. OZ is  bis of AB
65. a) 144
b) 121
66. 105
67. 57
68. BD  AC
69. 72
70. 68
71. 72
72. AOB  DOC
73. HL
74. SAS
75. SSS, SAS
76. ASA, SAS
77. SAS
78. HL
79. ASA
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
E
B
B
B
C
D
C
B
C
C
D
A
A
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
E
D
D
D
B
A
B
A
C
E
D
80. SSS, SAS, ASA
81. None
111. B
112. B
82. ASA
113. E
83.
84.
85.
86.
114. E
115. a) 140
b) 58
116. 24
SAS
None
C
C