Geometry - Chapter 5 Review PDF

Name: ________________________ Class: ___________________ Date: __________ ID: A Geometry - Chapter 5 Review 1. Points B, D, and F are midpoints of the sides of 3. Find the value of x. The diagram is not to scale. ACE. EC = 30 and DF = 17. Find AC....

Name: ________________________ Class: ___________________ Date: __________ ID: A Geometry - Chapter 5 Review 1. Points B, D, and F are midpoints of the sides of 3. Find the value of x. The diagram is not to scale. ACE. EC = 30 and DF = 17. Find AC. The diagram is not to scale. A. 90 B. 70 C. 35 D. 48 A. 60 4. Use the information in the diagram to determine the B. 30 height of the tree. The diagram is not to scale. C. 34 D. 8.5 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 Name: ________________________ ID: A 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 7. The length of DE is shown. What other length can Building in San Francisco, California, is 149 feet at you determine for this diagram? 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? 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 Name: ________________________ ID: A 8. Which statement can you conclude is true from the 10. Q is equidistant from the sides of TSR. Find given information? mRST. The diagram is not to scale.   Given: AB is the perpendicular bisector of IK. A. AJ = BJ A. 21 B. IAJ is a right angle. B. 42 C. IJ = JK C. 4 D. A is the midpoint of IK. D. 8  9. DF bisects EDG. Find the value of x. The 11. Q is equidistant from the sides of TSR. Find the diagram is not to scale. value of x. The diagram is not to scale. A. 285 A. 2 4 B. B. 12 19 C. 14 C. 32 D. 24 D. 19 3 Name: ________________________ ID: A 12. Which diagram shows a point P an equal distance 13. Where can the perpendicular bisectors of the sides from points A, B, and C? of a right triangle intersect? A. 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 Name: ________________________ ID: A 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 16. In ACE, G is the centroid and BE = 18. Find BG the triangle and AC = 26. and GE. A. BG  6, GE  12 B. BG  12, GE  6 A. 13 1 1 C. BG = 4 , GE = 13 B. 26 2 2 C. 52 D. BG = 9, GE = 9 D. not enough information 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 Name: ________________________ ID: A 18. Name a median for ABC. 21. Which labeled angle has the greatest measure? The diagram is not to scale. A. AD B. CE A. 1 C. AF B. 2 D. BD C. 3 D. not enough information in the diagram 19. Where can the medians of a triangle intersect? I. inside the triangle 22. Name the smallest angle of ABC. The diagram is II. on the triangle not to scale. 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. A A. incenter B. B circumcenter C. C centroid D. Two angles are the same size and smaller than orthocenter the third. B. circumcenter incenter 23. Three security cameras were mounted at the corners centroid of a triangular parking lot. Camera 1 was 156 ft orthocenter from camera 2, which was 101 ft from camera 3. C. circumcenter Cameras 1 and 3 were 130 ft apart. Which camera incenter had to cover the greatest angle? orthocenter A. camera 2 centroid B. camera 1 D. incenter C. camera 3 circumcenter D. cannot tell orthocenter centroid 6 Name: ________________________ ID: A 24. Name the second largest of the four angles named in 27. Which three lengths CANNOT be the lengths of the the figure (not drawn to scale) if the side included by sides of a triangle? 1 and 2 is 11 cm, the side included by 2 and A. 23 m, 17 m, 14 m 3 is 16 cm, and the side included by 3 and 1 is B. 11 m, 11 m, 12 m 14 cm. 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 29. Two sides of a triangle have lengths 6 and 17. B. 4 Which expression describes the length of the third C. 2 side? D. 1 A. at least 11 and less than 23 B. at least 11 and at most 23 25. mA  9x  7, mB  7x  9, and mC  28  2x. C. greater than 11 and at most 23 List the sides of ABC in order from shortest to D. greater than 11 and less than 23 longest. 30. Two sides of a triangle have lengths 5 and 12. A. AB; AC; BC Which inequalities represent the possible lengths for B. BC ; AB; AC the third side, x? C. AC; AB; BC A. 5  x  12 D. AB; BC ; AC B. 7  x  5 C. 7  x  17 26. List the sides in order from shortest to longest. The D. 7  x  12 diagram is not to scale. A. JK , LJ , LK B. LK , LJ , JK C. JK , LK , LJ D. LK , JK , LJ 7 Name: ________________________ ID: A 31. Which of the following must be true? 33. What is the range of possible values for x? The diagram is not to scale. The diagram is not to scale. A. AB  BC A. 0  x  54 B. AC  FH B. 0  x  108 C. BC  FH C. 0  x  27 D. AC  FH D. 27  x  180 32. If mDBC  73, what is the relationship between 34. What is the range of possible values for x? AD and CD? 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 Name: ________________________ ID: A 35. Identify parallel segments in the diagram. 9  ID: A Geometry - Chapter 5 Review Answer Section 1. ANS: C PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 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 OBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 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 OBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 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 OBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 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 OBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 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 OBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 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  ID: A 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 NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c 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 OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c TOP: 5-6 Problem 1 Applying the Corollary KEY: corollary to the Triangle Exterior Angle Theorem 2  ID: A 22. ANS: B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c TOP: 5-6 Problem 2 Using Theorem 5-10 23. ANS: C PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c 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 OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c 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 OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c 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 OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c TOP: 5-6 Problem 3 Using Theorem 5-11 27. ANS: D PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c 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 OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c 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 OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c 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 OBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c 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 NAT: CC G.CO.10| G.3.c TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem 3  ID: A 35. ANS: BD  AE, DF  AC, BF  CE PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c TOP: 5-1 Problem 1 Identifying Parallel Segments KEY: midsegment | parallel lines | Triangle Midsegment Theorem 4