Geometry - Chapter 5 Review

Class: Date: Geometry - Chapter 5 Review 1. Points B, D, and F are midpoints of the sides of ACE. EC = 30 and DF = 17. Find AC. The diagram is not to scale. 3. Find the value of x. The diagram is not to scale. A. 60 B. 30 C. 34 D. 8.5 A. 90 B. 70 C. 35 D. 48 4. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 2. Find the value of x. A. 75 ft B. 150 ft C. 35.5 ft D. 37.5 ft A. 7 B. 11.5 C. 8 D. 10 1

5. Use the information in the diagram to determine the measure of the angle x formed by the line from the point on the ground to the top of the building and the side of the building. The diagram is not to scale. A. 52 B. 26 C. 104 D. 38 6. A triangular side of the Transamerica Pyramid Building in San Francisco, California, is 149 feet at its base. If the distance from a base corner of the building to its peak is 859 feet, how wide is the triangle halfway to the top? 7. The length of DE is shown. What other length can you determine for this diagram? A. DF = 12 B. EF = 6 C. DG = 6 D. No other length can be determined. A. 298 ft B. 74.5 ft C. 149 ft D. 429.5 ft 2

8. Which statement can you conclude is true from the given information? 10. Q is equidistant from the sides of TSR. Find m RST. The diagram is not to scale. Given: AB is the perpendicular bisector of IK. A. AJ = BJ B. IAJ is a right angle. C. IJ = JK D. A is the midpoint of IK. 9. DF bisects EDG. Find the value of x. The diagram is not to scale. A. 21 B. 42 C. 4 D. 8 11. Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale. A. 285 B. 4 19 C. 32 D. 19 A. 2 B. 12 C. 14 D. 24 3

12. Which diagram shows a point P an equal distance from points A, B, and C? A. 13. Where can the perpendicular bisectors of the sides of a right triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. II only C. I or II only D. I, II, or II B. C. D. 4

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 = 26. 16. In ACE, G is the centroid and BE = 18. Find BG and GE. A. 13 B. 26 C. 52 D. not enough information A. BG 6, GE 12 B. BG 12, GE 6 C. BG = 4 1 2, GE = 131 2 D. BG = 9, GE = 9 17. In ABC, centroid D is on median AM. AD x 4 and DM 2x 4. Find AM. A. 13 B. 4 C. 12 D. 6 5

18. Name a median for ABC. 21. Which labeled angle has the greatest measure? The diagram is not to scale. A. AD B. CE C. AF D. BD 19. 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 20. For a triangle, list the respective names of the points of concurrency of perpendicular bisectors of the sides bisectors of the angles medians lines containing the altitudes A. incenter circumcenter centroid orthocenter B. circumcenter incenter centroid orthocenter C. circumcenter incenter orthocenter centroid D. incenter circumcenter orthocenter centroid A. 1 B. 2 C. 3 D. not enough information in the diagram 22. Name the smallest angle of ABC. The diagram is not to scale. A. A B. B C. C D. Two angles are the same size and smaller than the third. 23. Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 156 ft from camera 2, which was 101 ft from camera 3. Cameras 1 and 3 were 130 ft apart. Which camera had to cover the greatest angle? A. camera 2 B. camera 1 C. camera 3 D. cannot tell 6

24. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by 1 and 2 is 11 cm, the side included by 2 and 3 is 16 cm, and the side included by 3 and 1 is 14 cm. 27. Which three lengths CANNOT 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 28. Which three lengths could be the lengths of the sides of a triangle? A. 12 cm, 5 cm, 17 cm B. 10 cm, 15 cm, 24 cm C. 9 cm, 22 cm, 11 cm D. 21 cm, 7 cm, 6 cm A. 3 B. 4 C. 2 D. 1 25. m A 9x 7, m B 7x 9, and m C 28 2x. List the sides of ABC in order from shortest to longest. A. AB; AC; BC B. BC ; AB; AC C. AC; AB; BC D. AB; BC ; AC 26. List the sides in order from shortest to longest. The diagram is not to scale. 29. 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 30. Two sides of a triangle have lengths 5 and 12. Which inequalities represent the possible lengths for the third side, x? A. 5 x 12 B. 7 x 5 C. 7 x 17 D. 7 x 12 A. JK, LJ, LK B. LK, LJ, JK C. JK, LK, LJ D. LK, JK, LJ 7

31. Which of the following must be true? The diagram is not to scale. 33. What is the range of possible values for x? The diagram is not to scale. A. AB BC B. AC FH C. BC FH D. AC FH 32. If m DBC 73, what is the relationship between AD and CD? A. 0 x 54 B. 0 x 108 C. 0 x 27 D. 27 x 180 34. What is the range of possible values for x? The diagram is not to scale. A. AD CD B. AD CD C. AD CD D. not enough information A. 12 x 48 B. 0 x 10 C. 10 x 50 D. 10 x 43 8

35. Identify parallel segments in the diagram. 9

Geometry - Chapter 5 Review Answer Section 1. ANS: C PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint midsegment Triangle Midsegment Theorem 2. ANS: C PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint midsegment Triangle Midsegment Theorem 3. ANS: B PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles TOP: 5-1 Problem 2 Finding Lengths KEY: midsegment Triangle Midsegment Theorem 4. ANS: A PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles TOP: 5-1 Problem 3 Using a Midsegment of a Triangle KEY: midsegment Triangle Midsegment Theorem problem solving 5. ANS: A PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles TOP: 5-1 Problem 3 Using a Midsegment of a Triangle KEY: midsegment Triangle Midsegment Theorem problem solving 6. ANS: B PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles TOP: 5-1 Problem 3 Using a Midsegment of a Triangle KEY: midsegment Triangle Midsegment Theorem word problem problem solving 7. ANS: B PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectors NAT: CC G.CO.9 CC G.CO.12 CC G.SRT.5 G.3.c TOP: 5-2 Problem 1 Using the Perpendicular Bisector Theorem KEY: equidistant perpendicular bisector Perpendicular Bisector Theorem 8. ANS: C PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectors NAT: CC G.CO.9 CC G.CO.12 CC G.SRT.5 G.3.c TOP: 5-2 Problem 1 Using the Perpendicular Bisector Theorem KEY: equidistant perpendicular bisector Perpendicular Bisector Theorem reasoning 9. ANS: D PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectors NAT: CC G.CO.9 CC G.CO.12 CC G.SRT.5 G.3.c TOP: 5-2 Problem 3 Using the Angle Bisector Theorem KEY: Angle Bisector Theorem angle bisector 10. ANS: B PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectors NAT: CC G.CO.9 CC G.CO.12 CC G.SRT.5 G.3.c TOP: 5-2 Problem 3 Using the Angle Bisector Theorem KEY: Converse of the Angle Bisector Theorem angle bisector 1

11. ANS: A PTS: 1 DIF: L2 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectors NAT: CC G.CO.9 CC G.CO.12 CC G.SRT.5 G.3.c TOP: 5-2 Problem 3 Using the Angle Bisector Theorem KEY: angle bisector Converse of the Angle Bisector Theorem 12. ANS: A PTS: 1 DIF: L2 REF: 5-3 Bisectors in Triangles OBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectors NAT: CC G.C.3 G.3.c TOP: 5-3 Problem 1 Finding the Circumcenter of a Triangle KEY: circumcenter of the triangle circumscribe point of concurrency 13. ANS: B PTS: 1 DIF: L4 REF: 5-3 Bisectors in Triangles OBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectors NAT: CC G.C.3 G.3.c TOP: 5-3 Problem 1 Finding the Circumcenter of a Triangle KEY: circumcenter of the triangle perpendicular bisector reasoning right triangle 14. ANS: C PTS: 1 DIF: L3 REF: 5-3 Bisectors in Triangles OBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectors NAT: CC G.C.3 G.3.c TOP: 5-3 Problem 3 Identifying and Using the Incenter of a Triangle KEY: angle bisector incenter of the triangle point of concurrency 15. ANS: A PTS: 1 DIF: L2 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle TOP: 5-4 Problem 1 Finding the Length of a Median KEY: median of a triangle 16. ANS: A PTS: 1 DIF: L3 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle TOP: 5-4 Problem 1 Finding the Length of a Median KEY: centroid of a triangle median of a triangle 17. ANS: C PTS: 1 DIF: L4 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle TOP: 5-4 Problem 1 Finding the Length of a Median KEY: centroid of a triangle median of a triangle 18. ANS: D PTS: 1 DIF: L3 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle TOP: 5-4 Problem 2 Identifying Medians and Altitudes KEY: median of a triangle 19. ANS: A PTS: 1 DIF: L3 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle TOP: 5-4 Problem 2 Identifying Medians and Altitudes KEY: median of a triangle centroid of a triangle reasoning 20. ANS: B PTS: 1 DIF: L3 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle TOP: 5-4 Problem 3 Finding the Orthocenter KEY: angle bisector circumcenter of the triangle centroid of a triangle orthocenter of the triangle median altitude of a triangle perpendicular bisector 21. ANS: C PTS: 1 DIF: L2 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 1 Applying the Corollary KEY: corollary to the Triangle Exterior Angle Theorem 2

22. ANS: B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 2 Using Theorem 5-10 23. ANS: C PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 2 Using Theorem 5-10 KEY: word problem problem solving 24. ANS: D PTS: 1 DIF: L4 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 2 Using Theorem 5-10 KEY: corollary to the Triangle Exterior Angle Theorem 25. ANS: A PTS: 1 DIF: L4 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 3 Using Theorem 5-11 KEY: multi-part question 26. ANS: B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 3 Using Theorem 5-11 27. ANS: D PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 4 Using the Triangle Inequality Theorem KEY: Triangle Inequality Theorem 28. ANS: B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 4 Using the Triangle Inequality Theorem KEY: Triangle Inequality Theorem 29. ANS: D PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 5 Finding Possible Side Lengths KEY: Triangle Inequality Theorem 30. ANS: C PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle TOP: 5-6 Problem 5 Finding Possible Side Lengths KEY: Triangle Inequality Theorem 31. ANS: D PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two Triangles OBJ: 5-7.1 To apply inequalities in two triangles TOP: 5-7 Problem 1 Using the Hinge Theorem 32. ANS: C PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two Triangles OBJ: 5-7.1 To apply inequalities in two triangles TOP: 5-7 Problem 1 Using the Hinge Theorem 33. ANS: C PTS: 1 DIF: L2 REF: 5-7 Inequalities in Two Triangles OBJ: 5-7.1 To apply inequalities in two triangles TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem 34. ANS: D PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two Triangles OBJ: 5-7.1 To apply inequalities in two triangles TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem 3

35. ANS: BD AE, DF AC, BF CE PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles TOP: 5-1 Problem 1 Identifying Parallel Segments KEY: midsegment parallel lines Triangle Midsegment Theorem 4