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Quarter 2 Review – Geometry
PART I. True or False.
If the statement is FALSE, write the word or phrase that will make the statement TRUE.
1. If the measure of one acute angles of a right triangle is 54, then the other acute angle is 46.
2. If the legs of a right triangle are congruent, then each acute angle has a measure of 45.
3. Corresponding parts of congruent triangles are congruent.
4. An equilateral triangle is isosceles.
5. An obtuse triangle has three obtuse angles.
6. SSA is a method to prove a triangle congruent.
7. Acute angles are less than or equal to 90.
8. All equiangular triangles are equilateral.
9. The acute angles in a right triangle are supplementary.
10. All right triangles are congruent.
11. A right triangle has at least one right angle.
12. The hypotenuse of a right triangle is the side adjacent to the right angle.
13. The base angles of an isosceles triangle are complementary.
14. The legs of an isosceles triangle are equal in length.
15. The sum of the measures of the angles in a triangle is 360.
16. AA is a method to prove triangles congruent.
17. An isosceles triangle has at least two congruent sides.
18. A scalene triangle has no congruent sides.
19. The hypotenuse of a right triangle is the side opposite the right angle.
20. The segment connecting the midpoints of the two sides of a triangle is parallel to the third side and
half as long.
21. The leg of a right triangle is the longest side.
22. Two triangles are congruent if corresponding angles are congruent.
23. Vertical angles are congruent.
24. If ABC  DEF, then
AB CA

.
DE FD
25. AAS~ is a similarity theorem
26. SAS~ is a similarity theorem
27. Two congruent figures are always similar.
28. The geometric mean of 3 and 12 is
6
PART II. Multiple Choice.
Choose the best answer. Show all work used to obtain your answer. If necessary, draw a picture.
29. The statement “If mA = mB, then mB = mA” illustrates which property:
A. reflexive
B. symmetric
C. transitive
D. commutative
30. The number of right angles in a right triangle is:
A. 0
B. 1
C. 2
31. If m1 = 105, then m4 =
A. 105
B. 75
C. 95
D. 3
D. 65
32. Which of the following can NOT be used to prove that two triangles are congruent?
A. SSS
B. SSA
C. SAS
D. AAS
33. ABE  CBE. In CBA which part of ABE corresponds to BEC?
A. A
B. EBA
C. BCE
D. BEA
For #34-37, Use the diagram to determine the method that can be used to prove ABCEDC.
34. Given BD; BC  DC .
A. SSS
B. SAS
C. ASA
D. AAS
35. Given BC  DC ; AC  EC
A. AAS
B. SSS
C. SAS
D. ASA
36. Given A and E are right angles, BC  DC .
A. HL
B. AAS
C. SSS
D. SSA
37. Given AB  DE , AC  EC and A and E are right angles.
A. AAS
B. SSS
C. SAS
D. HL
38. 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
39. 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
40. 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
41. 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
42. The lengths of the legs of an isosceles triangle are 3x and x + 12. Find x.
A. 18
B. 12
C. 6
D. 4
43. 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
44. The side opposite the right angle in a right triangle is called the________________________.
A. base
B. vertex
C. hypotenuse
D. leg
45. A triangle with no congruent sides is called a(n) ______________ triangle.
A. equiangular
B. isosceles
C. obtuse
D. scalene
A
46. Given:
AC  AB; DC  DB
Which could be used to prove
ABD 
C
B
ACD?
D
If 3 sides of one triangle are congruent to 3
sides of another triangle, then the triangles are congruent.
A.
SSS
B.
SAS
If 2 sides and the angle between them in one triangle are congruent to 2
sides and the angle between them in another triangle, then the triangles are congruent.
C.
ASA
If 2 angles and the side of one triangle are congruent to 2 angles and the
of another triangle then the 2 triangles are congruent.
D.
AAS
If 2 angles and a side not between them are congruent to 2 angles and a
side not between them of another triangle, then the triangles are congruent.
47. In
a.
b.
c.
d.
similar polygons, corresponding angles are congruent and corresponding sides are:
congruent
oblique
proportional
unimportant
PART III. Free Response.
9
6
48. Find the value of x.
x
4
A
E
10
y
49. Given that ABC  EDF, solve for x and y:
6
B
50. Find z:
C
6
D
x
4
F
25
z
8
51.
B
12
If BD  8, DA  4, BE  10, and EC  5,
D
E
is DE || AC ?
A
C
52. Given triangle ABC with a line drawn parallel to AC intersecting AB at D and CB at E.
If AB = 8, BC = 12, and BD = 6, find BE.
53. Use
GHJ , where D, E, and F are midpoints of the sides. If DE  4x  5 , and GJ  3x  25 , what is GJ ?