Download Part VII: Free Response. Solve for the indicated values. Show all

Geometry
Q3 Test Review
Name _________________
(DO NOT LOSE THIS PACKET)
Date ______________
Part I: Determine whether each statement is true (T) or false (F).
T F
1. If the measure of one acute angle of a right triangle is 30°, then the measure of the other
acute angle is 60°.
T F
2. If the legs of a right triangle are congruent, each acute angle has a measure of 45°.
T F
3. The hypotenuse of a 45°-45°-90° triangle is
T F
4. A dodecagon has twenty sides.
T F
5. The measure of each interior angle of a regular hexagon is 120°.
T F
6. The sine ratio is defined to be the ratio of the length of the adjacent leg to the length of the
hypotenuse.
2 times as long as a leg.
Part II: Determine whether each statement is ALWAYS (A), SOMETIMES (S), or NEVER (N) true.
7. The diagonals of a quadrilateral are ___________ perpendicular.
8. The bases of a trapezoid are ___________ parallel.
9. “Proven” is ___________ a reason in a proof.
10. The exterior angles in a triangle _____________ add up to 360°.
Part III: Multiple Choice. Choose the BEST answer and place it in the space provided.
____ 11. If the length of the shorter leg of a 30°-60°-90° triangle is 4, then the length of the
hypotenuse is
a. 2
b. 4 3
c. 4 2
d. 8
C
____ 12. If AD = 3 and DB = 27, find CD.
a. 6 2
c. 40.5
b. 9
d. 81
B
D
C
A
____ 13. If BC = 15 and BD = 10, find AD.
a. 6.66
c. 22.5
b. 12.5
d. 125
B
D
A
M
____ 14. For MNO, the length of NO is
10
a. 5 2
c. 10
b. 5 3
d. 10 3
30
O
N
____ 15. If the sides of a triangle are 3, 4, and 6, then the triangle is
a. a 30°-60°-90° triangle
c. a 45°-45°-90° triangle
b. an acute triangle
d. not a right triangle
____ 16. If the length of the hypotenuse of a 45°-45°-90° triangle is 8, then the length of a leg is
a. 8 2
b. 4 2
c. 4
d. 4 3
R
For 17 and 18, use the diagram to the right.
____ 17. In RST, if mS  90, then tan R =
a.
TS
RS
b.
RS
TS
c.
TS
RT
d.
RS
RT
____ 18. In RST, if mS  90, then sin T =
a.
TS
RT
b.
RS
TS
c.
RS
RT
S
T
R
d.
RT
RS
S
T
____ 20. The length of a diagonal of a square is 6. The length of each side is
a. 6 2
b. 3 2
c. 6
d. 3
C
____ 21. If AD = 2.5, and AB = 10, find BC.
a. 6
b. 8
c. 5 3
d. 8 3
A
____ 22. If AD = 7 and AB = 28, find AC.
a. 14
b. 21
c. 4
C
A
D
B
d. 28
D
B
Part VI: Select the best answer from the list.
____ 33. Find x.
A. 12 3
y
x
B. 48.6°
6
____ 34. Find y.
C. 6 2
D. 6 3
____ 35. Find a.
E. 6
b
a
30
18
____ 36. Find b.
f
____ 37. Find e.
40
e
____ 38. Find f.
30
F. 41.4°
Part VII: Free Response. Solve for the indicated values. Show all work. Round answers to
the nearest tenth, when appropriate.
x
39. Find x and y.
124
108 y
65
40. A triangle has side lengths of 6, 9, and 11. Decide whether it is an acute, right, or obtuse
triangle. Explain.
41. Find the exact values of x and y. (No decimals!)
y
14
30
x
42. Find the value of x, to the nearest whole number. (not drawn to scale)
D
53
x
F
4
E
43. Find the sum of the measures of the interior angles of a decagon.
44. Find the number of sides of a regular polygon with each interior angle equal to 150°.
45. Find the measure of an interior and an exterior angle of a regular polygon with 15 sides.
46. An 8 foot ladder is leaning against a house and makes a 48° angle with the ground. How far is
the foot of the ladder from the house?
47. If the legs of a right triangle have the measures 5 and 8, what is the length of the hypotenuse?