Indicate whether the statement is true or false.
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1 Math 121 Fall Practice Exam - Chapters 5 & 6 Indicate whether the statement is true or false. 1. The simplified form of the ratio 6 inches to 1 foot is 6:1. 2. The triple (20,21,29) is a Pythagorean Triple. 3. Given that quadrilateral quadrilateral MNPQ,. 4. The most simplified form of the extended ratio 30 : 60 : 90 is 15 : 30 : In a circle in which m m, it follows that. 6. If, then. 7. In the proportion, the number b is known as the geometric mean for a and c. 8. The triple (13,15,18) is a Pythagorean Triple. Copyright Cengage Learning. Powered by Cognero. Page 1
2 9. Congruent circles have the same length of radius while concentric circles have the same center. 10. Any two squares are similar to each other. 11. Where m = x and and are tangents to the circle, m. 12. Given that, CSSTP leads to the extended proportion. 13. The triangle with sides of lengths a = 4, b = 5, and c = 7 is an obtuse triangle. 14. Two circles that are internally tangent have three common tangent lines. 15. A line through the center of a circle perpendicular to a chord (not a diameter) bisects the chord. Indicate the answer choice that best completes the statement or answers the question. Copyright Cengage Learning. Powered by Cognero. Page 2
3 16. In, m = 103 and m = 77. Which statement is false? a. is a semicircle b. would be a diameter c. is a minor arc d. would be a right angle 17. In the figure, chords and intersect at point X. If RX = 8, TX = 12, and XS = 9, find XV. a. 5.6 b. 6 c. 7.5 d. None of These 18. In,. Also,. Find. a. 30 b. 45 c. 60 d. None of These Copyright Cengage Learning. Powered by Cognero. Page 3
4 19. In the circle, m = 68 and m = 74. Find m. a. 34 b. 37 c. 71 d Given that,,, and, find PQ. a. 3 b. 8 c d The owner and a partner in a small business share profits in the ratio 2:1. For a month in which the business realizes a profit of $15,600. what is the owner s share of the profit? a. $5,200 b. $7,800 c. $10,400 d. None of These 22. Which type of triangle has sides of lengths a = 8, b = 15, and c = 17? a. acute b. right c. obtuse d. No triangle with these lengths of sides exists. 23. In, and. If, find. a. 6 b. Copyright Cengage Learning. Powered by Cognero. Page 4
5 c. d In, m = 138. Find m. a. 64 b. 69 c. 138 d. None of These 25. In the figure, a bird (at point B) is 36 feet above the ground. Meg is 60 feet from the bird while Mara is 39 feet from the bird. How far apart are Meg and Mara? a. 60 feet b. 61 feet c. 63 feet d. 99 feet Copyright Cengage Learning. Powered by Cognero. Page 5
6 26. In, m = 60 and BC = 12. Find AB. a. 3 b. c. 6 d. 27. Where,, and, determine the Pythagorean Triple generated by and. a. (45,28,53) b. (47,53,56) c. (10,18,28) d. (20,21,29) 28. The measures of the three interior angles of are in the ratio 2:3:7. What type of triangle is? a. acute b. right c. obtuse d. isosceles 29. Which statement is true? a. Any two equilateral triangles are similar. b. Any two equilateral triangles are congruent. c. Any two rectangles are similar. d. Any two rectangles are congruent. 30. Point P lies in the exterior of so that is tangent to the circle. Also, is a secant that intersects at B and C, where P-B-C. If PB = 9 and BC = 7, find PA. a. 10 b. 12 c. 16 d. None of These 31. In, the length of radius is 6 inches. If m = 90 and m = 60, how much longer is chord than chord? Copyright Cengage Learning. Powered by Cognero. Page 6
7 32. The figure shows right triangle ABC with. Also,. Where,,,, and, what reason allows you to conclude that? 33. In, chord diameter. With chords and, quadrilateral RSTV is formed. Being as specific as possible, what type of quadrilateral is RSTV? 34. In a circle, chords and intersect at point X. If m = 98, m = 54, and m = 72, which chord among,,, and would be longest? 35. Suppose that you have proved that and, in turn, that. What reason would you use to further conclude that? 36. If m = 105 and m = 73, find the measure of (not shown). 37. What is the consumption rate for a vehicle that travels a distance of 240 miles while consuming 10 gallons of gasoline? 38. In an equilateral triangle, each side measures 12 cm. Find the length of the altitude of this triangle. Copyright Cengage Learning. Powered by Cognero. Page 7
8 39. In the circle, m = 102 and m = 76. Where M is the midpoint of, find m. 40. Find the measure of the angle formed by the hands of a clock at exactly 4:10 PM. 41. For a given circle, tangent is drawn from external point E so that point T is the point of tangency. Where E-R-S, secant intersects that circle at points R and S. Find an expression that is equivalent to. 42. Diameter of is perpendicular to chord at point E. If CD = 18 and OE = 5, find the length of. 43. In isosceles triangle RST,. If, find the length of. 44. In a triangle, the length of a leg is the number a. What expression represents the length of the hypotenuse of this triangle? 45. In, and. If the length of is represented by 2a, find an expression for the length of. Copyright Cengage Learning. Powered by Cognero. Page 8
9 46. In the figure,. What reason allows you to conclude that? 47. In the figure, secants and intersect the circle at points R and S respectively. If m = 36 and m : m = 4:1, find m. 48. What does the question mark represent in this extended proportion? Copyright Cengage Learning. Powered by Cognero. Page 9
10 49. Given that, the two triangles are similar. Which side of corresponds to side of the second triangle? 50. From an external point E, tangents and are drawn to. If m = 78, find the measure of minor arc. 51. Supply missing statements and missing reasons for the following proof. Given: In the circle, Prove: S1. R1. S2. Draw R2. S3. R3. S4. R4. Congruent angles have equal measures. S5.? and? R5. The measure of an inscribed angle equals one-half the measure of its intercepted arc. S6. R6. S7. R7. Copyright Cengage Learning. Powered by Cognero. Page 10
11 S8. R Use the drawing provided to explain the Theorem. In a triangle whose angles measure 45, 45, and 90, the hypotenuse has a length equal to the product of and the length of either leg. Given:,, and Prove: with and 53. Supply all statements and all reasons for the proof that follows. Given: ; Prove: Copyright Cengage Learning. Powered by Cognero. Page 11
12 54. Use the drawing(s) to explain the Theorem. In a triangle whose angles measure 30, 60, and 90, the hypotenuse has a length equal to twice the length of the shorter leg, and the length of the longer leg is the product of and the length of the shorter leg. Given: Right,, and ; also, Prove: and with 55. Supply missing statements and missing reasons for the following proof. Given: Chords,,, and as shown Copyright Cengage Learning. Powered by Cognero. Page 12
13 Prove: S1. R1. S2. R2. S3. R3. If 2 inscribed intercept the same arc, these are. S4. R Supply missing statements and missing reasons for the following proof. Given: ; chords and intersect at point V Prove: S1. R1. S2. Draw and. R2. S3. R3. Vertical angles are congruent. S4. R4. S5. R5. AA S6. R6. S7. R7. Means-Extremes Property of a Proportion 57. Supply missing statements and missing reasons for the following proof. Copyright Cengage Learning. Powered by Cognero. Page 13
14 Given: Chords and intersect at point N in Prove: ) S1. R1. S2. Draw R2. S3. R3. The measure of an ext. of a is the sum of measures of the two nonadjacent int.. S4. and R4. S5. R5. Substitution Property of Equality S6. R6. Substitution Property of Equality 58. Supply missing statements and missing reasons for the proof of this theorem. The altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other. Given: Right triangle ABC with rt. ; Prove: S1. R1. S2. R2. S3. and are comp. R3. The acute angles of a rt. are comp. S4. and are comp. R4. S5. R5. If 2 s are comp. to the same, these are. S6. R6. Copyright Cengage Learning. Powered by Cognero. Page 14
15 Answer Key 1. False 2. True 3. True 4. False 5. True 6. True 7. True 8. False 9. True 10. True 11. True 12. True 13. True 14. False 15. True 16. c 17. b 18. a 19. c 20. b 21. c 22. b 23. b 24. b 25. c Copyright Cengage Learning. Powered by Cognero. Page 15
16 26. d 27. a 28. c 29. a 30. b 31. inches 32. CSSTP 33. isosceles trapezoid Means-Extremes Property mpg SAS eggs Copyright Cengage Learning. Powered by Cognero. Page 16
17 51. S1. In the circle, R1. Given R2. Through 2 points, there is exactly one line. R3. If 2 parallel lines are cut ny a transversal, the alternate interior angles are congruent. S4. S5. and R6. Substitution Property of Equality R7. Multiplication Property of Equality S8. R8. If 2 arcs of a circle are equal in measure, these arcs are congruent. 52. In,. Thus, the sides opposite these angles are congruent. If, then With the right angle at C, we apply the Pythagorean Theorem to obtain. Then, so. Applying the Square Roots Property, we have or. Then. 53. S1. ; R1. Given S2. and R2. The measure of a central angle of a circle is equal to the measure of its intercepted arc. S3. R3. Substitution Property of Equality 54. We reflect across to create an equiangular (and equilateral) triangle ( ). The reflection of, namely ) is conruent to. Then and by the Sement-Addition Postulate,, so Knowing that is equilateral, we have (completing the first part of the proof). Using the Pythagorean Theorem in, or, so or (completing the final part of the proof) 55. S1. Chords,,, and as shown R1. Given R2. Vertical angles are congruent. S3. (or ) S4. R4. AA 56. S1. ; chords and intersect at point V R1. Given R2. Through 2 points, there is exactly one line. S3. Copyright Cengage Learning. Powered by Cognero. Page 17
18 R4. If 2 inscribed angles of a circle intersect the same arc, these angles are congruent. S5. R6. CSSTP S S1. Chords and intersect at point N in R1. Given R2. Through 2 points, there is exactly one line. R4. In a circle, the measure of an inscribed angle is one-half that of its intercepted arc. S5. S6. ) 58. S1. Right triangle ABC with rt. ; R1. Given R2. Perpendicular lines meet to form right angles. R4. The acute angles of a rt. are comp. S5. S6. R6. AA Copyright Cengage Learning. Powered by Cognero. Page 18
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