Name ______________________________________________
Quarter 2 Test Review
Part I – Fill in the blank with the best answer.
1. In a triangle, the smallest angle is opposite (across from) the ______________________.
2. A right triangle has ________ right angle(s) and ________ acute angle(s).
3. List all shortcuts for proving that 2 triangles are congruent:
________________________________________
4. List all shortcuts for proving that 2 triangles are similar:
________________________________________
5. Triangles with no congruent sides are ___________________.
6. Triangles with 2 congruent sides are ____________________. They will also have 2 congruent
_____________.
7. Triangles with 3 congruent sides are _____________________. They will also have 3 congruent
_____________.
8. Corresponding sides of congruent triangles are _____________________.
9. Corresponding sides of similar triangles are ________________________.
10. Corresponding angles of congruent triangles are ____________________.
11. Corresponding angles of similar triangles are _______________________.
12. The angles in a triangle sum to _________.
13. The hypotenuse of a right triangle is opposite the _________________________.
14. The congruent sides of an isosceles triangle are called its ___________.
15. If two sides of a triangle measure 4 in. and 6 in., then the third side must be between _____ and _____
inches.
16. In a triangle, the largest angle is opposite the _________________________________.
17. A __________________ of a triangle is a segment joining the midpoints of two sides of the triangle.
18. A midsegment of a triangle is __________________ to the third side of the triangle and ___________
of its length.
Part II – Chapter 4 (Triangle Theorems and Congruence)
Find the value of x and/or y.
19.
x = ____________
21.
20.
x = ____________
22.
x = _________ y = _________
23.
x = _________ y = _________
x = _________ y = _________
24.
x = __________ mCBD  _______
Classify the triangle by its angles: _________________
25.
26.
x = _________ y = _________
Which postulate or theorem, if any, can be used to prove that the 2 triangles are congruent?
27.
28.
Congruent? ______
Congruent? ______
If yes, name postulate or theorem: _________
If yes, name postulate or theorem: _________
29.
30.
Congruent? ______
Congruent? ______
If yes, name postulate or theorem: _________
If yes, name postulate or theorem: _________
31.
32.
Congruent? ______
Congruent? ______
If yes, name postulate or theorem: _________
If yes, name postulate or theorem: _________
Use the information to draw a diagram if necessary.
33. The measure of one base angle of an isosceles triangle is 47. Find the measure of the vertex angle.
A. 86
B. 47
C. 106
D. 53
34. In isosceles DEF, DE = EF. If DE = 3x – 6, DF = 2x + 2, and EF = x + 4, find the length of DF.
A. 7
B. 9
C. 12
D. 5
35. The measures of two angles of a triangle are 32 and 47. What is the measure of the third angle?
A. 79
B. 109
C. 180
D. 101
36. Find the values of x and y so that ABC  DEF by HL.
A. x=45, y=12 B. x=45, y=5 C. x=90, y=12 D. x=90, y=13
5
37. The lengths of the legs of an isosceles triangle are 3x and x + 12. Find x.
A. 18
B. 12
C. 6
D. 4
38. The measures of the angles of a triangle are x – 15, x, and x + 15. Find x.
A. 60
B. 55
C. 65
D. 45
Complete the proofs.
39. Given: QAB  PBA and QA  PB
Prove: QAB  PBA
Statements
Reasons
B
40. Given: M is the midpoint of AD and BC
Prove: BMA  CMD
Statements
Reasons
Part II – Chapter 6 (Ratio, Proportion, and Similarity)
41. The ratios of 3 angles in a triangle are 2:5:11. Find the measures of the angles.
Angles: _______________________
42. Find the geometric mean of 8 and 12. ___________
43.
44. Triangles ABC and DEF are similar. What is the measure of EF?
EF = ___________
45. Two similar triangles have a scale factor of 2:3. The smaller triangle has a perimeter of 24 inches.
What is the perimeter of the larger triangle?
Perimeter = __________
46. Given RSW
a.
TUW , which proportion is true?
SW
RS

UW TW
b.
RW SW

UW UW
c.
RS WS

TU WU
d.
RS SW

TU TW
47. Given PQR
WUN ; mR  78 , what is the measure of W ?
mW  ________
48. Given ABC
LMN , what is the length of AC ?
AC  ________
49. Which diagram shows a pair of similar triangles? State the postulate or theorem (shortcut) used.
a.
b.
c.
d.
50. Which shortcut (postulate/theorem) proves that the given
triangles are similar? ________
Complete the similarity statement:
JNK
_________
51. Given DE is parallel to CB , AD  6, DC  12, and DE  4 ,
what is the length of CB ?
CB  _______
Postulate/Theorem: ________
52. In the diagram, DC represents the height of a flagpole and CB
represents its shadow. FE is the height of a person casting a 7-foot
shadow at the same time of day.
What is the height of the flagpole, to the nearest tenth of a foot? ____________
53. Triangles CDE and NOP are similar. The perimeter of the smaller triangle CDE is 133. The lengths of
two corresponding sides on the triangles are 53 and 212. What is the perimeter of NOP?
Perimeter of NOP  _______
54. Find the value of z: __________
Part III – Chapter 5 (Midsegments, Triangle Inequality Theorems)
55. In ABC , mA  100, mB  30, mC  50 . List the sides from shortest to longest.
_______, _______, _______
56. List the sides of WXY in order from shortest to longest if the angles have the indicated measures:
mW  (4 x  1) mX  (7 x  3) mY  (3x  4)
_______, _______, _______
57. Two sides of a triangle are 16 and 22 cm in length. Give the range of possible lengths of the 3 rd side.
__________ < third side < ____________
58. Which of the following sets of lengths could form a triangle?
a. 6 cm, 4 cm, 1 cm
b. 1 ft, 1 ft, 2 ft
c. 5.5 in , 6.5 in, 12 in
d. 10 m, 13 m, 18 m
59. Three land marks are placed on a map at points H, I, and J. A triangle is formed by connecting these
markers by string so that HI = 150 ft, HJ = 245 ft, and IJ = 365 ft. Which statements are true about the
measures of HIJ ? Circle all that apply.
a. mH is the smallest
b. mH is the largest
c. mI is the smallest
d. mJ is the smallest
60. Two sides of a triangle are 7 cm and 4 cm. Which measure couold NOT be a length of the third side?
a. 10 cm
b. 4 cm
Write the inequality relating each pair of measures:
61. mPRQ ____ mPRS
62. mDBC ____ mABE
c. 12 cm
d. 8.5 cm
63. Use the Hinge Theorem to write and solve an inequality to describe
the possible values of x.
______  x  _______
64. Use GHJ , where D, E, and F are midpoints of the sides. If
DE  4x  5 , and GJ  3x  25 , what is GJ ?
GJ = _________