Geometry Final Exam REVIEW Fall 2015

Transcription

1 Geometry Final Exam REVIEW Fall 2015 Use the diagram to answer questions 1 and 2. Name: 6. Which theorem proves that lines j and k are parallel? 1. Which angles are vertical angles? A) 1 and 2 C) 3 and 5 B) 1 and 5 D) 1 and 4 2. Which angles are supplementary angles? A) 1 and 4 C) 1 and 5 B) 4 and 5 D) 2 and 3 A) alternate interior angles converse B) alternate exterior angles converse C) corresponding angles converse D) same side interior angles converse 7. Which information CANNOT be used to prove j k? 3. If m n, solve for x and both angles? x = x + 67 = x = 4. In the diagram below, find the value of x. A) 24 B) 12 C) 30 D) Which theorem proves that lines m and n are parallel? m n A) 7 3 C) 1 supplementary to 6 B) 1 5 D) 1 supplementary to 2 8. What is the measure of B? A) 90 B) 38 C) 104 D) Which best describes the triangle? A) scalene triangle B) isosceles triangle C) right triangle D) not enough information 10. If TK is a median, find KR if SR = 14 A) alternate interior angles converse B) alternate exterior angles converse C) corresponding angles converse D) same side interior angles converse A) 14 B) 3.5 C) 21 D) 7

2 11. What is the value of x? A) 5 B) 35 C) 10 D) What is the measure of XYZ? A) 142 B) 128 C) 118 D) If Δ ABC Δ DEF, which angle is congruent to C? A) D B) E C) F D) A 14. If Δ ABC Δ DEF, which segment is congruent to AAAA? A) DDDD B) DDDD C) EEEE D) AAAA 15. What is the value of the exterior angle? 17. If l mm, which could be one of the angle measures? A) 7 B) 10 C) 34 D) 44 (4x 6)º t (3x + 4)º l 18. Which theorem justifies the congruence statement Δ KNM Δ KLM? A) SSS B) ASA C) SAS D) ASA 19. Why is ΔABD Δ DEF? A) SSS B) ASA C) SAS D) AAS 20. Which postulate, if any, can be used to prove the pair of triangles congruent? A) SSS B) AAS C) SAS D) ASA m A) 125 B) 180 C) 65 D) What is m RST? 21. What is the length of BC? A) 3.5 B) 7 C) 10 D) 7.9 A) 24 B) 72 C) 108 D) 180

3 22. What is the length of US? A) 13 B) 52 C) 39 D) One angle of a parallelogram measures 10. What is the measure of the angle opposite it? A) 170 B) 60 C) 80 D) One angle of a parallelogram measure 125. What is the measure of its consecutive angle? 27. In the figure, m 5 = (5x - 7) and m 13 = (3x + 9). What is the value for x?. A) 2 B) 6 C) 8 D) not enough information 28. What is the equivalent to sin 33? A) cos 33 B) sin 57 C) cos 57 D) tan If ABCD is a rhombus, what is the m AOB? A) 125 B) 55 C) 25 D) Find the circumference of a circle with an area of 9Π mi 2 A) 12Π mi B) 10Π mi C) 6Π mi D) 8Π mi A) 30 B) 45 C) 60 D) Given DDDD = 9x + 6 and CCCC = 5x + 35, find x. 26. KLMJ is a parallelogram. What is the length of LM? A) 3 B) 36 C) 38 D) The two triangles are similar. Given SSSS = 8; find. PPPP 8

4 32. What is the perimeter of this triangle? 38. Which angle is the alternate exterior angle with 1? 33. What is the classification of QRS according to its angles? A) 1 B) 5 C) 7 D) Which do you know about 7 and 8? What theorem or postulate did you use? 34. What is the classification of PQS according to its angles? 40. In the figure l n and r is a transversal. Which of the following is NOT necessarily true? 35. What is m R? A) 27.3 B) 32.1 C) 64.9 D) Two sides of a triangle are 9.3 and 22. What is the length of the third side? A) 18.6 B) 9.3 C) 19.9 D) The two sides of a right triangle are 33 and 56 what is the hypotenuse? A) 8 2 B) 2 6 C) 5 3 D) Given that Δ ABC ~ ΔDEF, solve for x and y. A) x = 11.67, y = 13.5 B) x = 10.67, y = 14.5 C) x = 11.67, y = 14.5 D) x = 10.67, y = Harry Hawk is standing on a 150 ft tall tower and spots a rival mascot at an angle of depression of 29 o. What is the distance between Harry and the rival mascot?

5 43. A Cessna plane is 5280 feet horizontally from a runway where it needs to land. If it is flying at an altitude of 200 feet, what is the angle of depression to the runway? 49. Find the distance of DC. 44. Use your calculator to determine cos 23 o. A) 1.07 B) C) D) To the nearest tenth, the sides of a right triangle measure 15, 17, and 8. To the nearest degree, what is the measure of the smallest angle? 45. An aquarium in a restaurant is a rectangular prism and measures 3.5 ft by 4 ft by 2 ft. What is the volume of the aquarium? A) 11.5 C) 28 B) 24 D) An aquarium in a restaurant is a rectangular prism and measures 2.5 ft by 4 ft by 3 ft. What is the volume of the aquarium? 51. Given that the height of the building is 12 ft, to find the length of the ladder we can use a trig ratio. Which of the following is the correct trig ratio? 47. What is the volume of a square period if each side of the base it 21 inches and the height is 17 inches? A) sin 62 = xx 12 B) cos 62 = xx 12 C) cos 62 = 12 xx D) sin 62 = 12 xx 48. What is the volume of the pyramid below? A) 378 ft 3 B) 126 ft 3 C) 126Π ft 3 D) 195Π ft The legs of a right triangle measure 12 & 27. To the nearest tenth of a degree, what is the measure of the angle opposite the shortest side? A) 63.6 B) 26.4 C) 66.0 D) 24.0

6 53. One leg of a right triangle measures 5 and the hypotenuse measures 17. To the nearest tenth of a degree, what is the measure of the angle opposite the shortest side? A) 72.9 B) 16.4 C) 17.1 D) What is the volume of a cylinder 8 feet tall with a radius of 3 feet? (In terms of π and rounded to nearest tenth). 57. What is the volume of this cylinder? (In terms of π and rounded to nearest tenth). 54. ΔABC is the pre-image to image ΔA B C. Describe the transformation. A) Dilation by a scale factor of 1 3 B) Dilation by a scale factor of 2 C) Dilation by a scale factor of 3 D) Translation to the left 5 and What is the volume of a cone with a base radius of 6 meters and a height of 17 meters? (π and rounded) 59. What is the volume of this cone? (In terms of π and rounded to nearest tenth). 55. Write the Triangle Congruence Statement for the given triangles. Which method can be used to prove the triangles congruent? Why is BC EF? 60. What is the volume of this sphere? (In terms of π and rounded to nearest tenth). A) ΔABC ΔDEF; Side-Angle-Side (SAS); CPCTC B) ΔABC ΔDFE; Side-Angle-Side (SAS); CPCTC C) ΔABC ΔDEF; Hypotenuse-Leg (HL); CPCTC D) ΔABC ΔDFE; Angle-Side-Angle (SSS); CPCTC 61. Find EF. 62. If m SPR = 3y 5 and m SQR = y + 70, find m SPR.

7 63. Find the m KJH. For # tell which construction is being completed HHHH and HHHH are tangent to circle F. Find HG Find mlm Find the arc length of minor AAAA ; round your answer to the nearest tenth. A 72. B 67. Find the area of sector DEF. Give your answers in terms of π If a human s eyeball is shaped like a sphere with a diameter or 28 mm. A dog s eyeball is shaped like a sphere with a diameter of 18 mm. About how many times greater is the volume of a human s eyeball than the volume of a dog s eyeball? 74.

8 State if the triangles are similar. If so, state how you know they are similar and complete the similarity statement. ΔPQR ~ 76. A) similar; SSS similarity; ΔPGH B) similar; AA similarity; ΔPGH C) not similar D) similar; SAS similarity; Δ PHG 81. In a pair of similar triangles, corresponding angles are and corresponding sides are. A) congruent, proportional C) different, congruent B) congruent, congruent D) proportional, equal Find the measure of the arc or angle indicated. A) 28 B) 66 C) 52 D) State if the triangles are similar. If so, state how you know they are similar and complete the similarity statement. ΔLMN ~ A) similar; AA similarity; ΔDBC B) not similar C) similar; SAS similarity; ΔBCD D) similar; SAS similarity; Δ DBC 83. Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent. A) 45 B) 35 C) 50 D) Find the missing side lengths. Leave your answers as radicals in simplest form. A) m = 8 3, n = 8 3 B) m = 24, n = 8 C) m = 8 3, n = 8 D) m = 24, n = 8 3