Name: ________________________ Class: ___________________ Date: __________
ID: A
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. B. C. D. A. B. C. D.
60 30 34 8.5
90 70 35 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. B. C. D.
A. B. C. D.
7 11.5 8 10
1
75 ft 150 ft 35.5 ft 37.5 ft
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
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?
D. 38 7. The length of DE is shown. What other length can you determine for this diagram?
A. B. C. D.
A. B. C. D.
298 ft 74.5 ft 149 ft 429.5 ft
2
DF = 12 EF = 6 DG = 6 No other length can be determined.
Name: ________________________
ID: A 10. Q is equidistant from the sides of TSR. Find mRST. The diagram is not to scale.
8. Which statement can you conclude is true from the given information?
Given: AB is the perpendicular bisector of IK .
A. B. C. D.
AJ = BJ IAJ is a right angle. IJ = JK A is the midpoint of IK .
A. B. C. D.
21 42 4 8
11. Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale.
9. DF bisects EDG. Find the value of x. The diagram is not to scale.
A. 285 4 B. 19 C. 32 D. 19
A. B. C. D.
3
2 12 14 24
Name: ________________________
ID: A
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
Name: ________________________
ID: A
14. Name the point of concurrency of the angle bisectors.
A. A
B. B
C. C
16. In ACE, G is the centroid and BE = 18. Find BG and GE.
15. Find the length of AB, given that DB is a median of the triangle and AC = 26.
A. B. C. D.
D. not shown
A. BG 6, GE 12 B. BG 12, GE 6 1 1 C. BG = 4 , GE = 13 2 2 D. BG = 9, GE = 9
13 26 52 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.
A. B. C. D.
21. Which labeled angle has the greatest measure? The diagram is not to scale.
AD CE AF BD
A. B. C. D.
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
1 2 3 not enough information in the diagram
22. Name the smallest angle of ABC. The diagram is not to scale.
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. B. C. D.
A B C 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
Name: ________________________
ID: A
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. B. C. D.
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
3 4 2 1
25. mA 9x 7, mB 7x 9, and mC 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
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
26. List the sides in order from shortest to longest. The diagram is not to scale.
A. B. C. D.
JK , LJ , LK LK , LJ , JK JK , LK , LJ LK , JK , LJ
7
Name: ________________________
ID: A
31. Which of the following must be true? The diagram is not to scale.
A. B. C. D.
33. What is the range of possible values for x? The diagram is not to scale.
AB BC AC FH BC FH AC FH
A. B. C. D.
32. If mDBC 73, what is the relationship between AD and CD?
A. B. C. D.
0 x 54 0 x 108 0 x 27 27 x 180
34. What is the range of possible values for x? The diagram is not to scale.
AD CD AD CD AD CD not enough information
A. B. C. D.
8
12 x 48 0 x 10 10 x 50 10 x 43
Name: ________________________
ID: A
35. Identify parallel segments in the diagram.
9
ID: A
Geometry - Chapter 5 Review Answer Section 1. ANS: OBJ: TOP: 2. ANS: OBJ: TOP: 3. ANS: OBJ: TOP: 4. ANS: OBJ: TOP: KEY: 5. ANS: OBJ: TOP: KEY: 6. ANS: OBJ: TOP: KEY: 7. ANS: OBJ: NAT: TOP: KEY: 8. ANS: OBJ: NAT: TOP: KEY: 9. ANS: OBJ: NAT: TOP: 10. ANS: OBJ: NAT: TOP: KEY:
C PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 5-1 Problem 2 Finding Lengths KEY: midpoint | midsegment | Triangle Midsegment Theorem C PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 5-1 Problem 2 Finding Lengths KEY: midpoint | midsegment | Triangle Midsegment Theorem B PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 5-1 Problem 2 Finding Lengths KEY: midsegment | Triangle Midsegment Theorem A PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 5-1 Problem 3 Using a Midsegment of a Triangle midsegment | Triangle Midsegment Theorem | problem solving A PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 5-1 Problem 3 Using a Midsegment of a Triangle midsegment | Triangle Midsegment Theorem | problem solving B PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 5-1 Problem 3 Using a Midsegment of a Triangle midsegment | Triangle Midsegment Theorem | word problem | problem solving B PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors 5-2.1 To use properties of perpendicular bisectors and angle bisectors CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c 5-2 Problem 1 Using the Perpendicular Bisector Theorem equidistant | perpendicular bisector | Perpendicular Bisector Theorem C PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors 5-2.1 To use properties of perpendicular bisectors and angle bisectors CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c 5-2 Problem 1 Using the Perpendicular Bisector Theorem equidistant | perpendicular bisector | Perpendicular Bisector Theorem | reasoning D PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors 5-2.1 To use properties of perpendicular bisectors and angle bisectors CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c 5-2 Problem 3 Using the Angle Bisector Theorem KEY: Angle Bisector Theorem | angle bisector B PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors 5-2.1 To use properties of perpendicular bisectors and angle bisectors CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c 5-2 Problem 3 Using the Angle Bisector Theorem 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: OBJ: NAT: 23. ANS: OBJ: NAT: KEY: 24. ANS: OBJ: NAT: KEY: 25. ANS: OBJ: NAT: KEY: 26. ANS: OBJ: NAT: 27. ANS: OBJ: NAT: KEY: 28. ANS: OBJ: NAT: KEY: 29. ANS: OBJ: NAT: KEY: 30. ANS: OBJ: NAT: KEY: 31. ANS: OBJ: TOP: 32. ANS: OBJ: TOP: 33. ANS: OBJ: TOP: 34. ANS: OBJ: TOP:
B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 2 Using Theorem 5-10 C PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 2 Using Theorem 5-10 word problem | problem solving D PTS: 1 DIF: L4 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 2 Using Theorem 5-10 corollary to the Triangle Exterior Angle Theorem A PTS: 1 DIF: L4 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 3 Using Theorem 5-11 multi-part question B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 3 Using Theorem 5-11 D PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 4 Using the Triangle Inequality Theorem Triangle Inequality Theorem B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 4 Using the Triangle Inequality Theorem Triangle Inequality Theorem D PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 5 Finding Possible Side Lengths Triangle Inequality Theorem C PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle 5-6.1 To use inequalities involving angles and sides of triangles CC G.CO.10| G.3.c TOP: 5-6 Problem 5 Finding Possible Side Lengths Triangle Inequality Theorem D PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two Triangles 5-7.1 To apply inequalities in two triangles NAT: CC G.CO.10| G.3.c 5-7 Problem 1 Using the Hinge Theorem C PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two Triangles 5-7.1 To apply inequalities in two triangles NAT: CC G.CO.10| G.3.c 5-7 Problem 1 Using the Hinge Theorem C PTS: 1 DIF: L2 REF: 5-7 Inequalities in Two Triangles 5-7.1 To apply inequalities in two triangles NAT: CC G.CO.10| G.3.c 5-7 Problem 3 Using the Converse of the Hinge Theorem D PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two Triangles 5-7.1 To apply inequalities in two triangles NAT: CC G.CO.10| G.3.c 5-7 Problem 3 Using the Converse of the Hinge Theorem
3
ID: A 35. ANS: BD AE, DF AC, BF CE PTS: OBJ: TOP: KEY:
1 DIF: L2 REF: 5-1 Midsegments of Triangles 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c 5-1 Problem 1 Identifying Parallel Segments midsegment | parallel lines | Triangle Midsegment Theorem
4