Chapter 5 Practice Test

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1 hapter 5 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the value of x. The diagram is not to scale. 40 x a. 32 b. 50 c. 64 d is the midpoint of is the midpoint of and = 21. Find. The diagram is not to scale. a. 42 b. 21 c d Points,, and F are midpoints of the sides of = 30 and F = 23. Find. The diagram is not to scale. F

2 a. 30 b c. 60 d Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 150 ft a. 75 ft b. 150 ft c ft d ft 5. Find the value of x. 16 3x 4 a. 4 b. 8 c. 6.6 d Find the length of the midsegment. The diagram is not to scale x x + 44 a. 24 b. 0 c. 42 d The length of is shown. What other length can you determine for this diagram?

3 G 12 F a. F = 12 c. F = 24 b. G = 12 d. No other length can be determined. 8. Q is equidistant from the sides of Find the value of x. The diagram is not to scale. T Q S (2x + 24) 30 R a. 27 b. 3 c. 15 d bisects Find the value of x. The diagram is not to scale. 8x + 42 F 15x a ) ) 30 G b. 90 c. 30 d Which statement can you conclude is true from the given information? Given: is the perpendicular bisector of

4 I J K a. J = J c. IJ = JK b. is a right angle. d. is the midpoint of. 11. Which statement is not necessarily true? Given: is the bisector of J K L a. K = K c. K is the midpoint of. b. d. J = L 12. Q is equidistant from the sides of Find The diagram is not to scale. T Q S (4x + 5) (8x 11) R a. 21 b. 42 c. 4 d bisects Find FG. The diagram is not to scale.

5 n + 8 F ) 3n 4 ) G a. 15 b. 14 c. 19 d Find the center of the circle that you can circumscribe about the triangle. y 5 ( 3, 3) 5 5 x ( 3, 2) (1, 2) 5 a. ( 1 2, 1) b. ( 1, 1 2 ) c. ( 3, 1 2 ) d. ( 1, 2) 15. In, G is the centroid and = 9. Find G and G. G F a. G = 2 1 4, G = 63 c. 4 b. d. G = 4 1 2, G = Name a median for

6 ) ) F a. b. c. d. 17. Name the point of concurrency of the angle bisectors. a. b. c. d. not shown 18. Find the length of, given that is a median of the triangle and = 26. a. 13 c. 52 b. 26 d. not enough information 19. Which diagram shows a point P an equal distance from points,, and?

7 a. c. b. d. 20. What is the name of the segment inside the large triangle? a. perpendicular bisector c. median b. altitude d. midsegment 21. In centroid is on median. and Find M. a. 13 b. 4 c. 12 d Name the smallest angle of The diagram is not to scale a. b. c. Two angles are the same size and smaller than the third. d.

8 23. List the sides in order from shortest to longest. The diagram is not to scale. J K 64 L a. b. c. d. 24. Which three lengths could be the lengths of the sides of a triangle? a. 12 cm, 5 cm, 17 cm c. 9 cm, 22 cm, 11 cm b. 10 cm, 15 cm, 24 cm d. 21 cm, 7 cm, 6 cm 25. Which three lengths can NOT be the lengths of the sides of a triangle? a. 23 m, 17 m, 14 m c. 5 m, 7 m, 8 m b. 11 m, 11 m, 12 m d. 21 m, 6 m, 10 m 26. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side? a. c. x > 10 and x < 18 b. x > 8 and x < 28 d. 27. Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side, x? a. b. c. d. 28. and List the sides of in order from shortest to longest. a. b. c. d. Short nswer 29. Identify parallel segments in the diagram.

9 F is the midpoint of and is the midpoint of Solve for x, given and 31. Given: is the perpendicular bisector of IK. Name two lengths that are equal. I J K 32. In draw median FJ from F to the side opposite F.

10 H F G 33. an these three segments form the sides of a triangle? xplain. b c a ssay 34. and are perpendicular bisectors of each other. Find,,, and. Justify your answers Other 35. T is the midpoint of QR. U is the midpoint of QS. RS = 36 and m QUT = 85. What are TU and m QSR? xplain.

11 Q T U R S 36. Find F and G. For each length, explain your answer. If you cannot determine the length of one or both of the segments, write not enough information. 6 G F 37. Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third side? xplain.

12 hapter 5 Practice Test nswer Section MULTIPL HOI 1. NS: RF: 5-1 Midsegments of Triangles TOP: 5-1 xample 1 2. NS: RF: 5-1 Midsegments of Triangles TOP: 5-1 xample 1 3. NS: RF: 5-1 Midsegments of Triangles TOP: 5-1 xample 1 4. NS: RF: 5-1 Midsegments of Triangles TOP: 5-1 xample 5. NS: RF: 5-1 Midsegments of Triangles 6. NS: RF: 5-1 Midsegments of Triangles 7. NS: RF: 5-2 isectors in Triangles TOP: 5-2 xample 1 8. NS: RF: 5-2 isectors in Triangles TOP: 5-2 xample 2 9. NS: RF: 5-2 isectors in Triangle TOP: 5-2 xample NS: RF: 5-2 isectors in Triangles 11. NS: RF: 5-2 isectors in Triangles 12. NS: RF: 5-2 isectors in Triangles OJ: Perpendicular isectors and ngle isectors ST: GOM 2.0 GOM 4.0 GOM 5.0 TOP: 5-2 xample 2 KY: onverse of the ngle isector Theorem angle bisector 13. NS: RF: 5-2 isectors in Triangles TOP: 5-2 xample NS: RF: 5-3 oncurrent Lines, Medians, and ltitudes TOP: 5-3 xample NS: RF: 5-3 oncurrent Lines, Medians, and ltitudes TOP: 5-3 xample NS: RF: 5-3 oncurrent Lines, Medians, and ltitudes TOP: 5-3 xample NS: RF: 5-3 oncurrent Lines, Medians, and ltitudes 18. NS: RF: 5-3 oncurrent Lines, Medians, and ltitudes TOP: 5-3 xample NS: RF: 5-3 oncurrent Lines, Medians, and ltitudes TOP: 5-3 xample 2

13 20. NS: RF: 5-3 oncurrent Lines, Medians, and ltitudes TOP: 5-3 xample NS: RF: 5-3 oncurrent Lines, Medians, and ltitudes 22. NS: RF: 5-5 Inequalities in Triangles TOP: 5-5 xample NS: RF: 5-5 Inequalities in Triangles TOP: 5-5 xample NS: RF: 5-5 Inequalities in Triangles TOP: 5-5 xample NS: RF: 5-5 Inequalities in Triangles TOP: 5-5 xample NS: RF: 5-5 Inequalities in Triangles TOP: 5-5 xample NS: RF: 5-5 Inequalities in Triangles TOP: 5-5 xample NS: RF: 5-5 Inequalities in Triangles SHORT NSWR 29. NS: RF: 5-1 Midsegments of Triangles TOP: 5-1 xample NS: RF: 5-1 Midsegments of Triangles 31. NS: IJ and JK RF: 5-2 isectors in Triangles TOP: 5-2 xample NS: H J F G

14 RF: 5-3 oncurrent Lines, Medians, and ltitudes 33. NS: No; for three segments to form the sides of a triangle, the sum of the length of two segments must be greater than the length of the third segment. RF: 5-5 Inequalities in Triangles SSY 34. NS: [4] = 13 by the Perpendicular isector Theorem. = 5 by the Perpendicular isector Theorem. = 12 by the Perpendicular isector Theorem, so = + = = 24. by SS, so = = 13. [3] finds three lengths with correct explanations [2] finds two lengths with correct explanations [1] finds one length with correct explanation RF: 5-2 isectors in Triangles OTHR 35. NS: y the Triangle Midsegment Theorem, TU = 18. lso, ngle Postulate. so m QSR = 85 by the orresponding RF: 5-1 Midsegments of Triangles 36. NS: F: y the definition of perpendicular bisector, G is the perpendicular bisector of F. Therefore, by the Perpendicular isector Theorem, F = = 6. G: not enough information RF: 5-2 isectors in Triangles TOP: 5-2 xample NS: Let x be the length of the third side. y the Triangle Inequality Theorem, 6 + x > 8, > x, and 8 + x > 6. Solving each inequality, x > 2, x < 14, and x > 2, respectively, or 2 < x < 14. RF: 5-5 Inequalities in Triangles

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