Name: ________________________ Class: ___________________ Date: __________
Combined Geometry Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Identify the hypothesis and conclusion of this conditional statement:
If tomorrow is Thursday, then yesterday was Tuesday.
a. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was not Tuesday.
b. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is Thursday.
c. Hypothesis: Yesterday was not Tuesday. Conclusion: Tomorrow is Thursday.
d. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.
____
2. What is the converse and the truth value of the converse of the following conditional?
If an angle is a right angle, then its measure is 90.
a. If an angle is not a right angle, then its measure is 90.
False
b. If an angle is not a right angle, then its measure is not 90.
True
c. If an angle has measure 90, then it is a right angle.
False
d. If an angle has measure 90, then it is a right angle.
True
____
3. BD bisects ∠ABC. m∠ABC = 7x. m∠ABD = 3x + 25. Find m∠DBC.
a. 50
b. 125
c. 75
____
d.
175
d.
153
4. m∠3 = 37. Find m∠1.
a.
37
b.
143
c.
1
27
ID: A
Name: ________________________
____
5. Which statement is true?
a.
b.
c.
d.
____
____
28
b.
56
c.
84
d.
7. Classify ΔABC by its angles, when m∠A = 32, m∠B = 85, and m∠C = 63.
a. right
b. straight
c. obtuse
d.
152
acute
8. Find the value of x. The diagram is not to scale.
a.
____
∠CBA and ∠EBH are same-side angles.
∠EBH and ∠BED are same-side angles.
∠CBA and ∠HBE are alternate interior angles.
∠EBH and ∠BED are alternate interior angles.
6. Find the value of x for which l is parallel to m. The diagram is not to scale.
a.
____
ID: A
33
b.
162
c.
147
9. If BCDE is congruent to OPQR, then DE is congruent to
a.
PQ
b.
OR
c.
2
OP
?
d.
75
d.
QR
.
Name: ________________________
ID: A
____ 10. If ΔMNO ≅ ΔPQR, which of the following can you NOT conclude as being true?
a.
MN ≅ PR
b.
∠M ≅ ∠P
c.
NO ≅ QR
d.
∠N ≅ ∠Q
____ 11. The two triangles are congruent as suggested by their appearance. Find the value ofc. The diagrams are not to
scale.
a.
4
b.
5
c.
3
d.
38
The polygons are similar, but not necessarily drawn to scale. Find the values ofx and y.
____ 12. Triangles ABC and DEF are similar. Find the lengths of AB and EF.
a.
b.
AB = 2; EF = 10
AB = 10; EF = 2
c.
d.
AB = 20; EF = 4
AB = 4; EF = 20
____ 13. You are reducing a map of dimensions 2 ft by 3 ft to fit to a piece of paper 8 in. by 10 in. What are the
dimensions of the largest possible map that can fit on the page?
2
2
a. 6 in.by 10 in.
c. 8 in. by 6 in.
3
3
1
b. 5 in.by 10 in.
d. 8 in.by 10 in.
3
3
Name: ________________________
ID: A
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem
you used.
____ 14.
a.
b.
ΔABC ∼ ΔMNO; SSS
ΔABC ∼ ΔMNO; SAS
c.
d.
ΔABC ∼ ΔMNO; AA
The triangles are not similar.
Explain why the triangles are similar. Then find the value ofx.
____ 15.
a.
b.
1
3
1
AA Postulate; 13
3
SSS Postulate; 5
c.
SAS Postulate; 13
d.
AA Postulate; 5
1
3
1
3
____ 16. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
a.
2 7
b.
28
c.
4
4 10
d.
160
Name: ________________________
ID: A
____ 17. Find the values of the variables and the lengths of the sides of this kite.
a.
b.
x = 9, y = 13; 7, 15
x =13, y = 9; 7, 15
c.
d.
x = 9, y = 13; 11, 20
x =13, y = 9; 11, 11
____ 18. What is the most precise name for quadrilateral ABCD with vertices A(–5, 2), B(–3, 6), C(6, 6), and D(4, 2)?
a. quadrilateral
b. rectangle
c. parallelogram
d. rhombus
____ 19. For the parallelogram, if m∠2 = 5x − 21 and m∠4 = 3x − 5, find m∠3. The diagram is not to scale.
a.
161
b.
19
c.
171
d.
8
____ 20. In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x – 5, and HE = 2y + 3. Find the values of x and y. The
diagram is not to scale.
a.
x = 6, y = 3
b.
x = 2, y = 3
c.
5
x = 3, y = 2
d.
x = 3, y = 6
Name: ________________________
ID: A
____ 21. In the rhombus, m∠1 = 15x, m∠2 = x + y, and m∠3 = 30z. Find the value of each variable. The diagram is
not to scale.
a.
b.
x = 12, y = 84, z = 20
x = 6, y = 174, z = 20
c.
d.
x = 6, y = 84, z = 10
x = 12, y = 174, z = 10
Find the area. The figure is not drawn to scale.
____ 22.
a.
607.32 in.2
b.
36.7 in.2
c.
303.66 in.2
d.
77.2 in.2
____ 23. Find the area of a polygon with the vertices of (–2, 3), (1, 3), (5, –3), and (–2, –3).
a. 120 units2
b. 7 units2
c. 30 units2
d. 60 units2
Find the area of the trapezoid. Leave your answer in simplest radical form.
____ 24.
a.
63 cm2
b.
70 cm2
c.
6
24.5 cm2
d.
9 cm2
Name: ________________________
ID: A
____ 25. A kite has diagonals 4.7 ft and 5 ft. What is the area of the kite?
a. 11.75 ft2
b. 23.5 ft2
c. 4.85 ft2
d.
19.4 ft2
Find the area of the regular polygon. Give the answer to the nearest tenth.
____ 26. pentagon with side 10 cm
a.
344.1 cm2
b.
34.4 cm2
c.
137.6 cm2
d.
172 cm2
b.
129.4 cm 2
c.
246.2 cm 2
d.
139.8 cm 2
c.
arc ADB; 245°
d.
arc AB; 245°
____ 27. decagon with side 4 cm
a.
123.1 cm 2
____ 28. Name the minor arc and find its measure.
a.
arc ADB; 30°
b.
arc AB; 115°
____ 29. The circumference of a circle is 50π cm. Find the diameter, the radius, and the length of an arc of60°.
a. 100 cm; 25 cm; 120π cm
c. 25 cm; 50 cm; 4.2π cm
b. 50 cm; 25 cm; 8.3π cm
d. 50 cm; 100 cm; 4.2π cm
____ 30. Find the length of arc XPY. Leave your answer in terms of π .
a.
12π m
b.
24π m
c.
7
4π m
d.
720π m
Name: ________________________
ID: A
Find the area of the circle. Leave your answer in terms ofπ .
____ 31.
a.
9.61π m2
b.
4.805π m2
c.
9.2π m2
d.
2.4025π m2
c.
62.8 in.2
d.
31.4 in.2
____ 32. Find the area of the figure to the nearest tenth.
a.
5.2 in.2
b.
10 in.2
____ 33. A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the
boxes. Find the lateral area and the surface area of the box to the nearest whole number.
a.
111 cm 2 ; 257 cm 2
c.
223 cm 2 ; 257 cm 2
b.
111 cm 2 ; 169 cm 2
d.
223 cm 2 ; 169 cm 2
8
Name: ________________________
ID: A
Find the surface area of the cylinder in terms ofπ .
____ 34.
a.
330π cm 2
b.
180π cm 2
c.
310 cm 2
d.
460π cm 2
Find the surface area of the pyramid shown to the nearest whole number.
____ 35.
a.
85 ft 2
b.
145 ft 2
c.
9
60 ft 2
d.
25 ft 2
Name: ________________________
ID: A
____ 36. Find the surface area of the cone in terms ofπ .
a.
90π cm 2
b.
96 cm 2
c.
114π cm 2
d.
192π cm 2
Find the volume of the given prism. Round to the nearest tenth if necessary.
____ 37.
a.
308 ft 3
b.
301 ft 3
c.
298 ft 3
d.
312 ft 3
a.
2143.4 yd 3
b.
1750.1 yd 3
c.
4286.8 yd 3
d.
2475.0 yd 3
____ 38.
10
Name: ________________________
ID: A
Find the volume of the cylinder in terms ofπ .
____ 39.
a.
75π m 3
b.
60 m 3
c.
37.5π m 3
d.
187.5π m 3
____ 40. The volume of a cylinder is 980π in. 3 . The height of the cylinder is 20 in. What is the radius of the cylinder?
a. 7 in.
b. 49 in.
c. 327 in.
d. 18 in.
Find the volume of the square pyramid shown. Round to the nearest tenth as necessary.
____ 41.
a.
192 ft 3
b.
9216 ft 3
c.
11
4608 ft 3
d.
3072 ft 3
Name: ________________________
ID: A
Find the volume of the cone shown as a decimal rounded to the nearest tenth.
____ 42.
a.
552.9 m 3
b.
829.4 m 3
c.
1,244.1 m 3
d.
3,317.5 m 3
π.
Find the surface area of the sphere with the given dimension. Leave your answer in terms of
____ 43. diameter of 16 cm
a.
256π cm 2
b.
128π cm 2
c.
32π cm 2
d.
1024π cm 2
b.
900π m 2
c.
3,600π m 2
d.
450π m 2
____ 44. radius of 30 m
a.
1,800π m 2
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
____ 45.
a.
1,767 cm 3
b.
442 cm 3
c.
236 cm 3
d.
14,137 cm 3
____ 46. The volume of a sphere is 3000π m 3 . What is the surface area of the sphere to the nearest square meter?
a.
2158 m 2
b.
37,699 m 2
c.
12
165 m 2
d.
1079 m 2
Name: ________________________
ID: A
Find the length of the missing side. Leave your answer in simplest radical form.
____ 47.
a.
3 29 cm
b.
3 21 cm
c.
21 cm
d.
3 cm
____ 48. A triangle has sides of lengths 6, 2, and 7. Is it a right triangle? Explain.
c. no; 6 2 + 2 2 = 7 2
a. no; 6 2 + 2 2 ≠ 7 2
b. yes; 6 2 + 2 2 ≠ 7 2
d. yes; 6 2 + 2 2 = 7 2
____ 49. A triangle has side lengths of10 cm, 24 cm, and 33 cm. Classify it as acute, obtuse, or right.
a. acute
b. right
c. obtuse
____ 50. Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
a.
9 3
b.
9 2
c.
13
9 3
2
d.
9 2
2
Name: ________________________
ID: A
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
____ 51.
Not drawn to scale
a.
x = 24 3 , y = 8
c.
x = 24, y = 8 3
b.
x = 8 3 , y = 24
d.
x = 8, y = 24 3
Find the value of x. Round the length to the nearest tenth.
____ 52.
a.
2.1 cm
b.
10.7 cm
c.
4.5 cm
d.
2.3 cm
a.
6.3 ft
b.
6.5 ft
c.
13 ft
d.
9.3 ft
____ 53.
14
Name: ________________________
ID: A
____ 54.
a.
1151.8 m
b.
203.1 m
c.
1134.3 m
d.
34.7 m
Short Answer
55. Find the measure of each interior and exterior angle. The diagram is not to scale.
56. ΔPQR ≅ ΔTSR. List the six pairs of congruent corresponding parts.
15
57.
58.