Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which statement is not necessarily true? Name: Given: is the bisector of Draw JD and DL such that it makes triangle DJL. Then answer the question. 62 D J K L 45 k a. DK = KE b. c. K is the midpoint of. d. DJ = DL E a. 17 b. 73 c. 118 d. 107 4. Find the value of x. The diagram is not to scale. 72 2. What is the name of the segment inside the large triangle? 105 x a. 33 b. 162 c. 147 d. 75 5. Find the value of x. The diagram is not to scale. a. perpendicular bisector b. altitude c. median d. midsegment Given:,, S 3. Find the value of k. The diagram is not to scale. R T U
Name: a. 5 b. 24 c. 20 d. 40 6. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38 and the two congruent sides each measure 21 units? a. 71 b. 142 c. 152 d. 76 21 38 21 Drawing not to scale 7. Find the value of x. The diagram is not to scale. R S (3x 50) (7x) a. b. c. d. none of these T 8. Which two statements contradict each other? I. Jon, Elizabeth, and Franco read 27 books among them for a class. II. Franco read 6 books. III. None of the three students read more than 7 books. a. I and II b. I and III c. II and III U d. No two of the statements contradict each other. 9. Which two statements contradict each other? I. lies on plane PQR. II. Point S lies on plane PQR. III. does not lie on plane PQR. a. I and II b. I and III c. II and III d. No two of the statements contradict each other. 10. Which three lengths can NOT be the lengths of the sides of a triangle? a. 23 m, 17 m, 14 m b. 11 m, 11 m, 12 m c. 5 m, 7 m, 8 m d. 21 m, 6 m, 10 m 11. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side? a. b. x > 8 and x < 28 c. x > 10 and x < 18 d. 12. Two sides of a triangle have lengths 6 and 17. Which expression describes the length of the third side? a. at least 11 and less than 23 b. at least 11 and at most 23 c. greater than 11 and at most 23 d. greater than 11 and less than 23 13. and List the sides of in order from shortest to longest. a. < < b. < < c. < < d. < < 14. List the sides in order from shortest to longest. The diagram is not to scale.
) J 66 50 K Name: b. < < c. < < d. < < 15. A perpendicular is drawn inside of a triangle, based on that information, identify that type of triangle 64 L a. < < Short Answer 16. Can these three segments form the sides of a triangle? Explain. a. Scalene Triangle b. Obtuse Triangle c. Right Obtuse Triangle d. Isosceles Triangle b c 18. Name a median, altitude, and angle bisector for a M P Q. ) O R N 17. In ACE, G is the centroid and BE = 9. Find BG and GE. C B G D 19. Find the values of x and y. A F E
Name: A E y ( x 47 B D C Drawing not to scale 116 D F Drawing not to scale 22. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 20. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42? 150 ft 23. Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side, x? 21. Use the information in the figure. Find 24. Find the value of x.
Name: 16 3x 4
Name: Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L3 REF: 5-2 Bisectors in Triangles OBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors STA: CA GEOM 2.0 CA GEOM 4.0 CA GEOM 5.0 KEY: Perpendicular Bisector Theorem perpendicular bisector reasoning 2. ANS: D PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and Altitudes 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 3. ANS: B PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles STA: CA GEOM 12.0 CA GEOM 13.0 TOP: 3-4 Example 1 KEY: triangle sum of angles of a triangle 4. ANS: A PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.2 Using Exterior Angles of Triangles STA: CA GEOM 12.0 CA GEOM 13.0 TOP: 3-4 Example 3 KEY: triangle sum of angles of a triangle 5. ANS: D PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.2 Using Exterior Angles of Triangles STA: CA GEOM 12.0 CA GEOM 13.0 KEY: exterior angle 6. ANS: A PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: isosceles triangle Converse of Isosceles Triangle Theorem Triangle Angle-Sum Theorem 7. ANS: A PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: Isosceles Triangle Theorem isosceles triangle 8. ANS: B PTS: 1 DIF: L2 REF: 5-4 Inverses, Contrapositives, and Indirect Reasoning OBJ: 5-4.2 Using Indirect Reasoning STA: CA GEOM 2.0 TOP: 5-4 Example 4 KEY: indirect reasoning 9. ANS: C PTS: 1 DIF: L2 REF: 5-4 Inverses, Contrapositives, and Indirect Reasoning OBJ: 5-4.2 Using Indirect Reasoning STA: CA GEOM 2.0 TOP: 5-4 Example 4 KEY: indirect reasoning 10. ANS: D PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 4 11. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 5 12. ANS: D PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles
Name: TOP: 5-5 Example 5 13. ANS: A PTS: 1 DIF: L4 REF: 5-5 Inequalities in Triangles KEY: Theorem 5-11 multi-part question 14. ANS: C PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 3 KEY: Theorem 5-11 15. ANS: D PTS: 1 SHORT ANSWER 16. ANS: 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. PTS: 1 DIF: L3 REF: 5-5 Inequalities in Triangles 17. ANS: PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and Altitudes STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 3 KEY: centroid median of a triangle 18. ANS: PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and Altitudes STA: CA GEOM 2.0 CA GEOM 21.0 TOP: 5-3 Example 4 KEY: median of a triangle 19. ANS: PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: angle bisector isosceles triangle 20. ANS: 96 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: isosceles triangle Isosceles Triangle Theorem Triangle Angle-Sum Theorem word problem 21. ANS: 32
Name: PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: Isosceles Triangle Theorem Triangle Angle-Sum Theorem isosceles triangle 22. ANS: 75 ft PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Using Properties of Midsegments STA: CA GEOM 17.0 TOP: 5-1 Example 3 KEY: midsegment Triangle Midsegment Theorem problem solving 23. ANS: PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 5 24. ANS: 4 PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Using Properties of Midsegments STA: CA GEOM 17.0 KEY: midpoint midsegment Triangle Midsegment Theorem