Midterm Review Fall ‘12
True or False:
1. Every line segment has one and only one midpoint. _______
2. If two angles are equal, they are right angles. ______
3. If two angles are supplementary, then they are equal. ______
4. Two points determine one and only one plane. ______
5. An angle has one and only one bisector. ______
6. The sum of two acute angles is an obtuse angle. ______
7. If a triangle is equilateral, then it is isosceles. ______
8. Since the sum of 20°, 30°and 40° is 90°, then the angles are complementary. ______
9. Every equilangular triangle is isosceles. ______
10. The two acute angles of a right triangle are supplementary. ______
11. The intersection of two planes is a line. _______
12. CPCTC is used to prove two triangles are congruent. _______
13. The distance formula can be used to prove to segments are congruent. _______
14. The midpoint formula can be used to prove a segment in a triangle is a median. ______
15. “Prove” is a reason in a two-column proof. _______
16. Two triangles can be proven congruent using the AA Postulate. _______
17. Similar figures have congruent angles and sides. _______
1
18. The hypothesis follows “then” in a conditional statement. _______
19. The converse of a conditional statement is always true. _______
20. A counterexample is used to support an argument that a conditional is false. _______
Set up and solve the following word problems.
21. Two angles are supplementary. Find the angles if one angle is 45°more than twice the other
angle.
∠1=____________
∠2=____________
22. Two angles are complimentary. If one angle is 32° less than the other, find the angles.
∠1=____________
∠2=____________
23. Two angles are supplementary. Find the angles if one angle is 10°more than two- thirds the
other angle.
∠1=____________
∠2=____________
24. In a triangle, ∠B is 12° larger than ∠A. ∠C is equal to the sum of the first two angles. Find the
angles.
∠1=____________
∠2=____________
∠3=____________
2
25. ΔABC is isosceles and one of the base angles is 15° larger than the vertex angle. Find the
angles.
∠1=____________
∠2=____________
∠3=____________
26. In a triangle, ∠B is 2 times as large as m∠A. If <C is 4° less than <A, find all three angles.
∠1=____________
∠2=____________
∠3=____________
27. The exterior angle of a triangle is 6x-19. The one of the two remote interior angles is 3 less
than twice the other. Find the measure of the exterior angle.
____________
Solve the following angle problems:
m∠BED = 52°
m∠CED = 28°
m∠AEB = 18°
m∠ AEC=______
28.
A
B
C
E
D
3
29.
⃗⃗⃗⃗⃗
EB bisects AED
m AED = 74°
m BEC = 19°
m CED=_______
A
B
C
E
D
m∠AEB = 29° 14’
m∠CED = 31° 26’
m∠BEC = 24° 34’
m∠ AED=_________
30.
A
B
C
D
E
m< ABE = 83° 14’
m< ABC = 23° 48’
m< CBD = 27° 17’
m< DBE = __________
31.
A
C
D
E
B
4
⃗⃗⃗⃗⃗⃗ Bisects ∠ABE)
(BC
m∠ABD = 56°
m∠ DBE = 28°
m∠ ABC=_________
32.
A
C
D
E
B
Solve the following for interior and exterior angles in isosceles triangles.
33. ∆ABC is isosceles with base AC.
m∠A = 3x
m∠B = 4x
Find x = ______ m∠A= _______
m∠B = _____
m∠C=_____
B
A
C
34. ΔABC is isosceles with base AC.
m∠BCD = 110°
Find m∠A _______
m∠B ________
m∠ACB________
B
A
C
D
5
Draw the segment and then solve.
̅̅̅̅
35. B is the midpoint of 𝐴𝐶
AC = x + 3
AB = x
AC = _____
AB = _____
BC = _____
36.
AC = _____
AB = _____
BC = _____
B is between points A and C.
AB = 4x – 1
BC = 2x + 3
AC = 8x
Decide if the following pairs of triangles are congruent. If they are finish the congruence
statement and identify the theorem that proves they are congruent.
37. Δ DOG ≅ Δ __________ BY:____________________
C
D
A
O
G
T
38. Δ BID ≅ Δ____________
BY:____________________
I
B
D
R
6
39. Δ SAN≅ Δ____________
S
BY:____________________
N
A
E
K
40. Δ GTA ≅ Δ____________
BY:____________________
G
O
T
A
41. Δ ABD ≅ Δ____________
Given ∠ADB ≅ ∠CDB
BY:____________________
A
D
B
C
7
42. Δ ABC≅ Δ____________
BY:____________________
D
A
C
E
B
Use the following sketch to solve:
C
A
B
E
F
D
H
G
43. m∠ABF = 6x – 16
m∠BFH = 2x +28
Find X _____________
44. m∠DBF = 5x + 16
m∠BFH = 3x + 12
Find X______________
m∠EFB=___________ m∠CBD=____________
m∠ABF=___________
m∠EFB =___________
Solve:
45. If two lines are parallel and are cut by a transversal, two alternate interior angles represented
by 3x and 5x – 70. Find the angle measures.
8
46. If two lines are parallel and are cut by a transversal, two corresponding angles represented by
2x + 10 and 4x -50. Find the angle measures.
47. If two lines are parallel and are cut by a transversal, two same side interior angles represented
by 2x and 3x. Find the angle measures.
Use the following sketch for # 48 – 53.
A
E
G
7
5
8
F
6
3
1
B
4
2
C
D
H
48. List all Alternate Interior angles._____________________________
49. List all Alternate Exterior angles._____________________________
50. List all Corresponding angles.________________________________
51. List all Same side interior angles._____________________________
52. If m∠ABC = 108° then m∠GFH =_______; m∠HFB=_________________
53. If < DBF = 95°, then m∠BFH=________; m∠BFE=__________________
9
A
B
I
54.
AB CE FH
ABD  32
E
D
C
BDG  89
EDG  _________
G
F
55.
DGH  _________
H
E
AB CD
BFG  _________
F
A
B
FGD  _________
5x+16
G 3x+12
C
D
H
E
A
B
F
56. AB || CD
6x - 16
m<AFG = __________
m<FGD = __________
2x +28
G
C
D
H
A
57. BF || CD
EC bisects <ACD
m<EGF = 42°
m< CBF = __________
m< ABG = _________
E
B
C
10
G
F
D
Simplify each radical expression
58. 4√600
59. √
17
60. 4√96 - 2√54
3
Set up the following ratio and reduce to lowest terms.
61. 10 inches to 3 feet
___________________
62. 30 minutes to 5 hours
___________________
63. 5√3 to √27
___________________
Solve the proportion.
66.
68.
7
9

x 27
16 x

x 4
67.
4 3 2

3
x
69.
7 5
x

2 5 8 5
Find the geometric mean.
70. 4 and 12
71. 5x and 20x
72. 36 and 18
73. 2√3 and 5√3
11
Are the triangles similar? If so, write a similarity statement and identify the postulate or theorem that justifies your
answer.
74. Δ BCA ~ Δ____________
BY:____________________
B
E
92°
92°
23°
A
C
68°
D
F
75. Δ FLY ~ Δ____________
BY:____________________
L
E
8 cm
6 cm
15 cm
S
25 cm
10 cm
R
F
20 cm
Y
76. Δ LYF ~ Δ____________
BY:____________________
L
F
32°
E
9 cm
44 cm
12 cm
24 cm
Y
32°
R
S
12
̅̅̅̅ ∥ 𝐼𝐽
̅.
77. Given 𝐻𝐾
KJ = 5
HK = 6
IJ = 15
Find GJ = ____
I
H
G
K
J
78. Given ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐷𝐸 .
A
B
AB = 2√5
CB = 4√3
ED = 5√6
C
Find CD = ________
E
D
̅̅̅̅ .
̅̅̅̅̅ ∥ 𝐷𝐶
79. Find x and y in the diagram below if 𝐸𝐵
D
DC = 27
AD = 33
AB = 20
AC = 30
E
x
Find x = _____
Find y = _____
y
A
B
C
13
80. If ∆ABC~∆QPR, m∠A = 30° and m∠B = 97°, find the measures of angles Q, P, and R.
m < Q = _____
m < P = ______
m < R = ______
81-83 Use the diagram at the right to the answer the next 3 questions. A, B, and C are midpoints.
81. If AB=3x+8 and GJ=2x+24, what is AB? __________
82. If AC=3y-5 and HJ=4y+2, what is HB? __________
83. If GH=7z-1 and BC=4z-3, what is GH? __________
84-86. Is this triangle possible?
84. 2.5, 3.5, 5 ___________ 85. 2, 6, 9 __________
86. 9, 12, 15 _________
87-88. Find the third side. Write an inequality statement.
87. 5, 15, ___________________
88. 8, 22, __________________
89-90. Find all the missing angles.
89.
90.
C
D
34°
54°
A
B
E
77°
F
14
91-94 Use the diagram to the right.
91. If AB=BC, and m B=75, then the longest side is ____________.
92. If m A=90, then the longest side is ______________.
93. If AB=8, BC=6 and AC=13, then the largest angle is ______.
94. If AB=5, BC=7, and AC=10, then the smallest angle is ________.
Coordinate Plane Problems
95. Find the endpoint, B, of AB, if A(8,-4) and the midpoint is (5, -9).
B = ____________
96. Find the distance between A(2,4) and B(-12, 6).
Round your answer to the nearest tenth.
d = ____________
97-98 Use ∆𝑨𝑩𝑪
97. Classify this triangle. ____________________
98. Find the coordinates of the median from vertex B. ______________________
̅̅̅̅ _____________, ______________
99. Find the coordinates of the midsegment that is parallel to side 𝐴𝐶
15
100-102. Use ∆𝑫𝑬𝑭
100. Is the triangle equiangular? Justify your answer
101. Name the coordinate of the altitude from vertex E.
102. Are the triangles congruent? If so, name the congruence statement and justify with a postulate or theorem.
103. Given the following conditional, write the converse and determine if they are each true or false
If two angles are congruent, then they are vertical angles.
Converse: _____________________________________________________________________
Statement
T/F
Converse
16
T/F
104.
Given:
̅̅̅̅ ⊥ 𝐵𝐴
̅̅̅̅
𝐵𝐶
Statement 2: _____________________________________
Reason 2: _______________________________________
105. Write a proof.
̅̅̅̅ 𝑎𝑛𝑑 𝑊𝑍
̅̅̅̅̅
Given: X is the midpoint of 𝑉𝑌
Prove: VWX ≅ ∆YZX
STATEMENTS
REASONS
1.
1.
2.
2.
3.
3.
4.
4.
106. Write a proof.
Given: D is the midpoint of ̅̅̅̅
𝐴𝐶
∠𝐴𝐷𝐵 ≅ ∠𝐵𝐷𝐶
̅̅̅̅
Prove: ̅̅̅̅
𝐴𝐵 ≅ 𝐵𝐶
STATEMENTS
REASONS
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
17