Geometry
Quarter 3 Review
- This review covers the major topics in the material that will be included on the Quarter 3 Test. It is
not necessarily all inclusive and additional study and problem solving practice may be required to fully
prepare for the Quarter Test. There is a practice interactive achievement test available online as well.
Go to the BRHS website and on the left hand side go to itest. Enter your student ID and click on the
Quarter 3 review test! The Interactive Achievement practice test is optional.
- Use additional paper, if necessary.
This review is due on or before __________________________________
Name __________________________________
Teacher ________________________________
Period_______________________
Part I: Determine whether each statement is true (T) or false (F).
T F
1. If the measures 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. When a central angle and an inscribed angle intercept the same arc, the two angles are
congruent.
T F
5. A tangent to a circle is perpendicular to a radius drawn to the point of tangency.
T F
6. An angle inscribed in a semicircle is a right angle.
T F
7. If two circles are congruent, then their diameters are congruent.
T F
8. If a diameter is perpendicular to a chord, then it bisects the chord.
T F
9. All angles which intercept congruent arcs of a circle are congruent.
T F
10. The sine ratio is defined to be the ratio of the length of the adjacent leg to the length of
the hypotenuse.
T F
11. The area of a right triangle with side lengths of 3, 4, and 5 is 6 units.
T F
12. Opposite angles of an inscribed quadrilateral are complementary.
2 times as long as a leg.
Part II: Determine whether each statement is ALWAYS (A), SOMETIMES (S), or NEVER (N) true.
13. A radius of a circle is ___________ a chord of the circle.
14. The sine of an angle is ___________ greater than 1.
Part III: Multiple Choice. Choose the BEST answer and place it in the space provided.
____ 15. The geometric mean of 3 and 12 is
a. 2
b. 4
c. 6
d. 8
____ 16. 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
____ 17. Find the perimeter of a square whose area if 36.
a. 6
b. 12
c. 24
d. 36
____ 18. For MNO, the length of NO is
a. 5 2
c. 10
b. 5 3
d. 10 3
M
10
30
N
O
____ 19. If the perimeter of a square equals 20 2, the length of each diagonal of the square is
a. 10 2
b. 5 2
c. 10
d. 5
____ 20. 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
____ 21. 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
For 22 and 23, use the diagram to the right.
____ 22. In RST, if mS  90, then tan R =
a.
TS
RS
b.
RS
TS
c.
TS
RT
d.
RS
RT
R
____ 23. In RST, if mS  90, then sin T =
S
a.
TS
RT
b.
RS
TS
c.
RS
RT
d.
T
RT
RS
For 24 and 25, use circle R to the right.
____ 24. A major arc of circle R is
a. DEF
b. EF
D
G
c. DGF
E
d. ED
R
____ 25. In circle R, mGD  mDF 
a. mDEF
b. mGDE
c. mGFD
F
d. mGDF
For 26 – 28, use circle O to the right.
____ 26. The measure of ABC 
a. 100°
b. 90°
c. 80°
d. 70°
110
A
____ 27. The measure of A 
D
O
100
a. 40°
b. 50°
c. 60°
d. 70°
X
B
C
____ 28. The measure of AXD 
a. 85°
b. 95°
c. 55°
d. 100°
____ 29. Quadrilateral WXYZ is inscribed in circle P. If mX  80 and
mXW  105, then mXY 
a. 95°
b. 100°
c. 105°
W
X
P
d. 110°
Z
Y
For 30 and 31, use circle S to the right.
____ 30. If mFG  80 and mEC  44, then mD 
F
a. 62°
b. 38°
c. 22°
d. 18°
E
____ 31. If CX = 12, XG = 2, and XH = 3, then XF =
a. 12
b. 8
c. 4.5
S
X
D
d. 2
H
____ 32. 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
Part IV: Matching. Match each figure with its area.
____ 33.
____ 34.
3
4
A. 30
13
4
B. 24
3
C. 25
12
D. 2 3
____ 35.
E. 16 3
____ 36.
13
5
10
____ 37.
4
30
G
C
8
Part V: Matching. Match each part to its correct name. BE SPECIFIC!!
D
E
1
C
G
O
B
F
2
A
H
____ 38. CG
A. chord
____ 39. DE
B. secant
____ 40. D
C. diameter
____ 41. AB
D. point of tangency
____ 42. HF
E. tangent
____ 43. ODE
AB. inscribed angle
____ 44. 1
AC. central angle
____ 45. 2
AD. radius
____ 46. OD
AE. right angle
Part VI: Select the best answer from the list.
____ 47. Find x.
A. 12 3
y
x
B. 48.6
6
____ 48. Find y.
C. 6 2
D. 6 3
____ 49. Find a.
E. 6
b
a
30
18
____ 50. Find b.
____ 51. Find e.
40
e
30
Part VII: Free Response. Solve for the indicate values. Show all work. Round answers to
the nearest tenth, when appropriate.
52. A wheelchair ramp has a slope of
1
1
. If its rise is 5 feet, what is its run?
2
10
53. Find the area of this right triangle if b = 17 and c =
514.
c
a
b
54. A triangle has side lengths of 6, 9, and 11. Decide whether it is an acute, right, or obtuse
triangle. Explain.
55. Find the value of x and y.
y
14
30
x
56. Find the value of x, to the nearest whole number. (not drawn to scale)
D
53
x
F
4
E
57. Find mPQ in circle A. Drawing is not to scale.
(2y - 15)
P
Q
A
S
(y + 35)
R
58. What must be the measures of B and C so that a circle can circumscribed about ABCD?
(Diagram is not drawn to scale.)
C
B
103
78
D
A
59. Find the value of x if mAB  41 and mCD  35. (not drawn to scale)
D
O
x
A
B
C
60. 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?
61. If the legs of a right triangle have the measures 5 and 8, what is the length of the hypotenuse?
62. Given: Circle O with diameter containing points A(7, -2) and B(1, 6)
a) Determine the coordinates of the center. Show the work that leads to your solution.
b) Determine the length of the diameter. Show the work that leads to your solution.
c) Determine the length of the radius. Show
the work that leads to your solution.
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d) Determine the equation of the circle. Show
the work that leads to your solution.
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