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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 equilateral 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. _______
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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=____________
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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:
28.
m∠BED = 52°
m∠CED = 28°
m∠AEB = 18°
m∠ AEC=______
A
B
C
E
D
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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 ∠ABC)
(BE
m∠ABD = 56°
m∠ DBC = 28°
m∠ ABE=_________
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
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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
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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
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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.
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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=__________________
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A
B
I
54.
E
D
C
G
F
55.
H
E
F
A
AB CD
BFG  _________
FGD  _________
B
5x+16
G 3x+12
C
AB CE FH
ABD  32
BDG  89
EDG  _________
DGH  _________
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.
7
9

x 27
68.
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
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