# Ch 5 Practice Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 Name: Class: Date: Ch 5 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of x. The diagram is not to scale. a. 32 b. 50 c. 64 d B is the midpoint of AC, D is the midpoint of CE, and AE = 11. Find BD. The diagram is not to scale. a. 5.5 b. 11 c. 22 d

2 Name: 3. Points B, D, and F are midpoints of the sides of ACE. EC = 35 and DF = 23. Find AC. The diagram is not to scale. a. 70 b. 46 c d Find the value of x. a. 6 b. 5 c. 8.5 d Find the length of the midsegment. The diagram is not to scale. a b. 88 c. 44 d. 37 2

3 Name: 6. Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale. a. 27 b. 3 c. 15 d DF bisects EDG. Find the value of x. The diagram is not to scale. a b. 90 c. 30 d Which statement can you conclude is true from the given information? Given: AB is the perpendicular bisector of IK. a. AJ = BJ c. IJ = JK b. IAJ is a right angle. d. A is the midpoint of IK. 3

4 Name: 9. Find the center of the circle that you can circumscribe about the triangle. a. ( 1 2, 4) b. ( 3, 2) c. ( 1 2, 2) d. ( 2, 1 2 ) 10. Find the center of the circle that you can circumscribe about EFG with E(4, 4), F(4, 2), and G(8, 2). a. (6, 3) b. (4, 2) c. (4, 4) d. (3, 6) 11. Where can the bisectors of the angles of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. III only c. I or III only d. I, II, or II 12. In ACE, G is the centroid and BE = 12. Find BG and GE. a. BG = 4, GE = 8 c. BG = 8, GE = 4 b. BG = 3, GE = 9 d. BG = 6, GE = 6 4

5 Name: 13. Name a median for PQR. a. PU b. RT c. PS d. QS 14. Name the point of concurrency of the angle bisectors. a. A b. B c. C d. not shown 15. Find the length of AB, given that DB is a median of the triangle and AC = 30. a. 15 c. 60 b. 30 d. not enough information 16. Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. III only c. I or III only d. I, II, or II 5

6 Name: 17. What is the name of the segment inside the large triangle? a. median c. midsegment b. angle bisector d. perpendicular bisector 18. What is the name of the segment inside the large triangle? a. perpendicular bisector c. altitude b. median d. midsegment 19. In ABC, centroid D is on median AM. AD = x + 6 and DM = 2x 3. Find AM. a. 15 b. 16 c. 4 d What is the inverse of this statement? If she studies hard in math, she will succeed. a. If she will succeed, then she does not study hard in math. b. If she studies hard in math, she will not succeed. c. If she does not study hard in math, she will not succeed. d. If she does not study hard in math, she will succeed. 21. What is the contrapositive of this statement? If a figure has three sides, it is a triangle. a. If a figure does not have three sides, it is a triangle. b. If a figure is not a triangle, then it does not have three sides. c. If a figure has three sides, it is not a triangle. d. If a figure is a triangle, then it does not have three sides. 6

7 Name: 22. Name the smallest angle of ABC. The diagram is not to scale. a. A b. Two angles are the same size and smaller than the third. c. B d. C 23. List the sides in order from shortest to longest. The diagram is not to scale. a. LJ, LK, JK b. LJ, JK, LK c. JK, LJ, LK d. JK, LK, LJ 24. Which three lengths could be the lengths of the sides of a triangle? a. 19 cm, 6 cm, 7 cm c. 7 cm, 24 cm, 12 cm b. 10 cm, 13 cm, 22 cm d. 13 cm, 5 cm, 18 cm 25. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side? a. x 8 and x 28 c. x > 10 and x < 18 b. x > 8 and x < 28 d. x 10 and x Two sides of a triangle have lengths 9 and 16. What must be true about the length of the third side, x? a. 7 < x < 16 b. 9 < x < 16 c. 7 < x < 25 d. 7 < x < m A = 10x 5, m B = 5x 10, and m C = 52 2x. List the sides of ABC in order from shortest to longest. a. AB; BC; AC b. AC; AB; BC c. AB; AC; BC d. BC; AB; AC Short Answer 28. To prove p is equal to q using an indirect proof, what would your starting assumption be? 7

8 Ch 5 Practice Exam Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles OBJ: Using Properties of Midsegments STA: CA GEOM 17.0 TOP: 5-1 Example 1 KEY: midsegment Triangle Midsegment Theorem 2. ANS: A PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles OBJ: Using Properties of Midsegments STA: CA GEOM 17.0 TOP: 5-1 Example 1 KEY: midpoint midsegment Triangle Midsegment Theorem 3. ANS: B PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles OBJ: Using Properties of Midsegments STA: CA GEOM 17.0 TOP: 5-1 Example 1 KEY: midpoint midsegment Triangle Midsegment Theorem 4. ANS: A PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: Using Properties of Midsegments STA: CA GEOM 17.0 KEY: midpoint midsegment Triangle Midsegment Theorem 5. ANS: C PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: Using Properties of Midsegments STA: CA GEOM 17.0 KEY: midsegment Triangle Midsegment Theorem 6. ANS: B PTS: 1 DIF: L2 REF: 5-2 Bisectors in Triangles OBJ: Perpendicular Bisectors and Angle Bisectors STA: CA GEOM 2.0 CA GEOM 4.0 CA GEOM 5.0 TOP: 5-2 Example 2 KEY: angle bisector Converse of the Angle Bisector Theorem 7. ANS: D PTS: 1 DIF: L2 REF: 5-2 Bisectors in Triangles OBJ: Perpendicular Bisectors and Angle Bisectors STA: CA GEOM 2.0 CA GEOM 4.0 CA GEOM 5.0 TOP: 5-2 Example 2 KEY: Angle Bisector Theorem angle bisector 8. ANS: C PTS: 1 DIF: L3 REF: 5-2 Bisectors in Triangles OBJ: Perpendicular Bisectors and Angle Bisectors STA: CA GEOM 2.0 CA GEOM 4.0 CA GEOM 5.0 KEY: perpendicular bisector Perpendicular Bisector Theorem reasoning 9. ANS: C PTS: 1 DIF: L2 OBJ: Properties of Bisectors STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 1 KEY: circumscribe circumcenter of the triangle 10. ANS: A PTS: 1 DIF: L2 OBJ: Properties of Bisectors STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 1 KEY: circumcenter of the triangle circumscribe 11. ANS: A PTS: 1 DIF: L3 OBJ: Properties of Bisectors STA: CA GEOM 2.0 CA GEOM 21.0 KEY: incenter of the triangle angle bisector reasoning 12. ANS: A PTS: 1 DIF: L2 STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 3 KEY: centroid median of a triangle 1

9 13. ANS: D PTS: 1 DIF: L2 STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 4 KEY: median of a triangle 14. ANS: C PTS: 1 DIF: L2 STA: CA GEOM 2.0 CA GEOM 21.0 KEY: angle bisector incenter of the triangle point of concurrency 15. ANS: A PTS: 1 DIF: L2 STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 3 KEY: median of a triangle 16. ANS: A PTS: 1 DIF: L3 STA: CA GEOM 2.0 CA GEOM 21.0 KEY: median of a triangle centroid reasoning 17. ANS: B PTS: 1 DIF: L2 STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 4 KEY: altitude of a triangle angle bisector perpendicular bisector midsegment median of a triangle 18. ANS: A PTS: 1 DIF: L2 STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 4 KEY: altitude of a triangle angle bisector perpendicular bisector midsegment median of a triangle 19. ANS: A PTS: 1 DIF: L3 STA: CA GEOM 2.0 CA GEOM 21.0 KEY: centroid median of a triangle 20. ANS: C PTS: 1 DIF: L2 REF: 5-4 Inverses, Contrapositives, and Indirect Reasoning OBJ: Writing the Negation, Inverse, and Contrapositive STA: CA GEOM 2.0 TOP: 5-4 Example 2 KEY: contrapositive 21. ANS: B PTS: 1 DIF: L2 REF: 5-4 Inverses, Contrapositives, and Indirect Reasoning OBJ: Writing the Negation, Inverse, and Contrapositive STA: CA GEOM 2.0 TOP: 5-4 Example 2 KEY: contrapositive 22. ANS: C PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles OBJ: Inequalities Involving Angles of Triangles STA: CA GEOM 2.0 CA GEOM 6.0 TOP: 5-5 Example 2 KEY: Theorem ANS: D PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles OBJ: Inequalities Involving Sides of Triangles STA: CA GEOM 2.0 CA GEOM 6.0 TOP: 5-5 Example 3 KEY: Theorem ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles OBJ: Inequalities Involving Sides of Triangles STA: CA GEOM 2.0 CA GEOM 6.0 TOP: 5-5 Example 4 KEY: Triangle Inequality Theorem 25. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles OBJ: Inequalities Involving Sides of Triangles STA: CA GEOM 2.0 CA GEOM 6.0 TOP: 5-5 Example 5 KEY: Triangle Inequality Theorem 2

10 26. ANS: C PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles OBJ: Inequalities Involving Sides of Triangles STA: CA GEOM 2.0 CA GEOM 6.0 TOP: 5-5 Example 5 KEY: Triangle Inequality Theorem 27. ANS: C PTS: 1 DIF: L4 REF: 5-5 Inequalities in Triangles OBJ: Inequalities Involving Sides of Triangles STA: CA GEOM 2.0 CA GEOM 6.0 KEY: Theorem 5-11 multi-part question SHORT ANSWER 28. ANS: p is not equal to q. PTS: 1 DIF: L2 REF: 5-4 Inverses, Contrapositives, and Indirect Reasoning OBJ: Using Indirect Reasoning STA: CA GEOM 2.0 TOP: 5-4 Example 3 KEY: indirect reasoning indirect proof 3

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