Name: ________________________ Class: ___________________ Date: __________ ID: A

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Combined Geometry Review

Multiple ChoiceIdentify 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.

Falseb. If an angle is not a right angle, then its measure is not 90.

Truec. If an angle has measure 90, then it is a right angle.

Falsed. 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

____ 4. m∠3 = 37. Find m∠1.

a. 37 b. 143 c. 27 d. 153

Name: ________________________ ID: A

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____ 5. Which statement is true?

a. ∠CBA and∠EBH are same-side angles.b. ∠EBH and∠BED are same-side angles.c. ∠CBA and ∠HBE are alternate interior angles.d. ∠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. 28 b. 56 c. 84 d. 152

____ 7. Classify ΔABC by its angles, when m∠A = 32, m∠B = 85, and m∠C = 63.a. right b. straight c. obtuse d. acute

____ 8. Find the value of x. The diagram is not to scale.

a. 33 b. 162 c. 147 d. 75

____ 9. If BCDE is congruent to OPQR, then DE is congruent to ? .a. PQ b. OR c. OP d. QR

Name: ________________________ ID: A

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____ 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 of c. 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 of x and y.

____ 12. Triangles ABC and DEF are similar. Find the lengths of AB and EF.

a. AB = 2; EF = 10 c. AB = 20; EF = 4b. AB = 10; EF = 2 d. 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?

a. 623

in.by 10 in. c. 8 in. by 623

in.

b. 513

in.by 10 in. d. 8 in.by 10 in.

Name: ________________________ ID: A

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State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

____ 14.

a. ΔABC ∼ ΔMNO; SSS c. ΔABC ∼ ΔMNO; AAb. ΔABC ∼ ΔMNO; SAS d. The triangles are not similar.

Explain why the triangles are similar. Then find the value of x.

____ 15.

a. SSS Postulate; 513 c. SAS Postulate; 131

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b. AA Postulate; 1313 d. AA Postulate; 51

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____ 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 10 d. 160

Name: ________________________ ID: A

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____ 17. Find the values of the variables and the lengths of the sides of this kite.

a. x = 9, y = 13; 7, 15 c. x = 9, y = 13; 11, 20b. x =13, y = 9; 7, 15 d. 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. x = 3, y = 2 d. x = 3, y = 6

Name: ________________________ ID: A

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____ 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. x = 12, y = 84, z = 20 c. x = 6, y = 84, z = 10b. x = 6, y = 174, z = 20 d. 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. 24.5 cm2 d. 9 cm2

Name: ________________________ ID: A

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____ 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

____ 27. decagon with side 4 cm

a. 123.1 cm2 b. 129.4 cm2 c. 246.2 cm2 d. 139.8 cm2

____ 28. Name the minor arc and find its measure.

a. arc ADB; 30° b. arc AB; 115° c. arc ADB; 245° d. arc AB; 245°

____ 29. The circumference of a circle is 50π cm. Find the diameter, the radius, and the length of an arc of 60°.a. 100 cm; 25 cm; 120π cm c. 25 cm; 50 cm; 4.2π cmb. 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. 4π m d. 720π m

Name: ________________________ ID: A

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Find the area of the circle. Leave your answer in terms of π .

____ 31.

a. 9.61π m2 b. 4.805π m2 c. 9.2π m2 d. 2.4025π m2

____ 32. Find the area of the figure to the nearest tenth.

a. 5.2 in.2 b. 10 in.2 c. 62.8 in.2 d. 31.4 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 cm2; 257 cm2 c. 223 cm2 ; 257 cm2

b. 111 cm2; 169 cm2 d. 223 cm2 ; 169 cm2

Name: ________________________ ID: A

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Find the surface area of the cylinder in terms of π .

____ 34.

a. 330π cm2 b. 180π cm2 c. 310 cm2 d. 460π cm2

Find the surface area of the pyramid shown to the nearest whole number.

____ 35.

a. 85 ft2 b. 145 ft2 c. 60 ft2 d. 25 ft2

Name: ________________________ ID: A

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____ 36. Find the surface area of the cone in terms of π .

a. 90π cm2 b. 96 cm2 c. 114π cm2 d. 192π cm2

Find the volume of the given prism. Round to the nearest tenth if necessary.

____ 37.

a. 308 ft3 b. 301 ft3 c. 298 ft3 d. 312 ft3

____ 38.

a. 2143.4 yd3 b. 1750.1 yd3 c. 4286.8 yd3 d. 2475.0 yd3

Name: ________________________ ID: A

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Find the volume of the cylinder in terms of π .

____ 39.

a. 75π m3 b. 60 m3 c. 37.5π m3 d. 187.5π m3

____ 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 ft3 b. 9216 ft3 c. 4608 ft3 d. 3072 ft3

Name: ________________________ ID: A

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Find the volume of the cone shown as a decimal rounded to the nearest tenth.

____ 42.

a. 552.9 m3 b. 829.4 m3 c. 1,244.1 m3 d. 3,317.5 m3

Find the surface area of the sphere with the given dimension. Leave your answer in terms of π .

____ 43. diameter of 16 cm

a. 256π cm2 b. 128π cm2 c. 32π cm2 d. 1024π cm2

____ 44. radius of 30 m

a. 1,800π m2 b. 900π m2 c. 3,600π m2 d. 450π m2

Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.

____ 45.

a. 1,767 cm3 b. 442 cm3 c. 236 cm3 d. 14,137 cm3

____ 46. The volume of a sphere is 3000π m3 . What is the surface area of the sphere to the nearest square meter?

a. 2158 m2 b. 37,699 m2 c. 165 m2 d. 1079 m2

Name: ________________________ ID: A

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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.a. no; 62 + 22 ≠ 72 c. no; 62 + 22 = 72

b. yes; 62 + 22 ≠ 72 d. yes; 62 + 22 = 72

____ 49. A triangle has side lengths of 10 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.9 3

2d.

9 22

Name: ________________________ ID: A

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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 3b. 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

____ 53.

a. 6.3 ft b. 6.5 ft c. 13 ft d. 9.3 ft

Name: ________________________ ID: A

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____ 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.

Name: ________________________ ID: A

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57. Write a two-column proof to show that ΔOQR ≅ ΔMQR.Given: NO ≅ PM , ∠1 ≅ ∠2, and OR ≅ MR

58. Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.

Name: ________________________ ID: A

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Essay

59. Write a two-column proof.

Given: ∠2 and ∠5 are supplementary.Prove: l Ä m

60. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.

Name: ________________________ ID: A

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61. Write a two-column proof.Given: BC ≅ EC and AC ≅ DCProve: BA ≅ ED

62. Write a two-column proof:Given: ∠BAC ≅ ∠DAC, ∠DCA ≅ ∠BCAProve: BC ≅ CD

63. Write a proof.Given: AB ⋅ BE = CB ⋅ BDProve: ΔABC ∼ ΔDBE