Name: ________________________ Class: ___________________ Date: __________ ID: A

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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.

A. 60B. 30C. 34D. 8.5

2. Find the value of x.

A. 7B. 11.5C. 8D. 10

3. Find the value of x. The diagram is not to scale.

A. 90B. 70C. 35D. 48

4. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.

A. 75 ftB. 150 ftC. 35.5 ftD. 37.5 ft

Name: ________________________ ID: A

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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?

A. 298 ftB. 74.5 ftC. 149 ftD. 429.5 ft

7. The length of DE is shown. What other length can you determine for this diagram?

A. DF = 12B. EF = 6C. DG = 6D. No other length can be determined.

Name: ________________________ ID: A

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8. Which statement can you conclude is true from the given information?

Given: AB

is the perpendicular bisector of IK .

A. AJ = BJB. IAJ is a right angle.C. IJ = JKD. A is the midpoint of IK .

9. DF

bisects EDG. Find the value of x. The diagram is not to scale.

A. 285

B. 419

C. 32D. 19

10. Q is equidistant from the sides of TSR. Find mRST. The diagram is not to scale.

A. 21B. 42C. 4D. 8

11. Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale.

A. 2B. 12C. 14D. 24

Name: ________________________ ID: A

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12. Which diagram shows a point P an equal distance from points A, B, and C?A.

B.

C.

D.

13. Where can the perpendicular bisectors of the sides of a right triangle intersect? I. inside the triangleII. on the triangleIII. outside the triangleA. I onlyB. II onlyC. I or II onlyD. I, II, or II

Name: ________________________ ID: A

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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.

A. 13B. 26C. 52D. not enough information

16. In ACE, G is the centroid and BE = 18. Find BG and GE.

A. BG 6, GE 12B. BG 12, GE 6

C. BG = 412 , GE = 131

2D. BG = 9, GE = 9

17. In ABC, centroid D is on median AM . AD x 4 and DM 2x 4. Find AM.A. 13B. 4C. 12D. 6

Name: ________________________ ID: A

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18. Name a median for ABC.

A. ADB. CEC. AFD. BD

19. Where can the medians of a triangle intersect?I. inside the triangleII. on the triangleIII. outside the triangleA. I onlyB. III onlyC. I or III onlyD. 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 altitudesA. incenter

circumcentercentroidorthocenter

B. circumcenterincentercentroidorthocenter

C. circumcenterincenterorthocentercentroid

D. incentercircumcenterorthocentercentroid

21. Which labeled angle has the greatest measure? The diagram is not to scale.

A. 1B. 2C. 3D. not enough information in the diagram

22. Name the smallest angle of ABC. The diagram is not to scale.

A. AB. BC. CD. 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 2B. camera 1C. camera 3D. cannot tell

Name: ________________________ ID: A

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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.

A. 3B. 4C. 2D. 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; BCB. BC ; AB; ACC. AC; AB; BCD. AB; BC ; AC

26. List the sides in order from shortest to longest. The diagram is not to scale.

A. JK , LJ , LKB. LK , LJ , JKC. JK , LK , LJD. LK , JK , LJ

27. Which three lengths CANNOT be the lengths of the sides of a triangle?A. 23 m, 17 m, 14 mB. 11 m, 11 m, 12 mC. 5 m, 7 m, 8 mD. 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 cmB. 10 cm, 15 cm, 24 cmC. 9 cm, 22 cm, 11 cmD. 21 cm, 7 cm, 6 cm

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 23B. at least 11 and at most 23C. greater than 11 and at most 23D. 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 12B. 7 x 5C. 7 x 17D. 7 x 12

Name: ________________________ ID: A

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31. Which of the following must be true?The diagram is not to scale.

A. AB BCB. AC FHC. BC FHD. AC FH

32. If mDBC 73, what is the relationship between AD and CD?

A. AD CDB. AD CDC. AD CDD. not enough information

33. What is the range of possible values for x?The diagram is not to scale.

A. 0 x 54B. 0 x 108C. 0 x 27D. 27 x 180

34. What is the range of possible values for x?The diagram is not to scale.

A. 12 x 48B. 0 x 10C. 10 x 50D. 10 x 43

Name: ________________________ ID: A

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35. Identify parallel segments in the diagram.

ID: A

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Geometry - Chapter 5 ReviewAnswer Section

1. ANS: C PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.cTOP: 5-1 Problem 2 Finding Lengths KEY: midpoint | midsegment | Triangle Midsegment Theorem

2. ANS: C PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.cTOP: 5-1 Problem 2 Finding Lengths KEY: midpoint | midsegment | Triangle Midsegment Theorem

3. ANS: B PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.cTOP: 5-1 Problem 2 Finding Lengths KEY: midsegment | Triangle Midsegment Theorem

4. ANS: A PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.cTOP: 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 TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.cTOP: 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 TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.cTOP: 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 BisectorsOBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectorsNAT: 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 BisectorsOBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectorsNAT: 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 BisectorsOBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectorsNAT: 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 BisectorsOBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectorsNAT: 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

ID: A

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11. ANS: A PTS: 1 DIF: L2 REF: 5-2 Perpendicular and Angle BisectorsOBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectorsNAT: 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 TrianglesOBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c TOP: 5-3 Problem 1 Finding the Circumcenter of a TriangleKEY: circumcenter of the triangle | circumscribe | point of concurrency

13. ANS: B PTS: 1 DIF: L4 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c TOP: 5-3 Problem 1 Finding the Circumcenter of a TriangleKEY: circumcenter of the triangle | perpendicular bisector | reasoning | right triangle

14. ANS: C PTS: 1 DIF: L3 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c TOP: 5-3 Problem 3 Identifying and Using the Incenter of a TriangleKEY: angle bisector | incenter of the triangle | point of concurrency

15. ANS: A PTS: 1 DIF: L2 REF: 5-4 Medians and AltitudesOBJ: 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 MedianKEY: median of a triangle

16. ANS: A PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 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 MedianKEY: centroid of a triangle | median of a triangle

17. ANS: C PTS: 1 DIF: L4 REF: 5-4 Medians and AltitudesOBJ: 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 MedianKEY: centroid of a triangle | median of a triangle

18. ANS: D PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 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 AltitudesKEY: median of a triangle

19. ANS: A PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 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 AltitudesKEY: median of a triangle | centroid of a triangle | reasoning

20. ANS: B PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 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 OrthocenterKEY: 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 TriangleOBJ: 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 CorollaryKEY: corollary to the Triangle Exterior Angle Theorem

ID: A

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22. ANS: B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 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 TriangleOBJ: 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 5-10KEY: word problem | problem solving

24. ANS: D PTS: 1 DIF: L4 REF: 5-6 Inequalities in One TriangleOBJ: 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 5-10KEY: corollary to the Triangle Exterior Angle Theorem

25. ANS: A PTS: 1 DIF: L4 REF: 5-6 Inequalities in One TriangleOBJ: 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 5-11KEY: multi-part question

26. ANS: B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 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 TriangleOBJ: 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 TheoremKEY: Triangle Inequality Theorem

28. ANS: B PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 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 TheoremKEY: Triangle Inequality Theorem

29. ANS: D PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 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 LengthsKEY: Triangle Inequality Theorem

30. ANS: C PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 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 LengthsKEY: Triangle Inequality Theorem

31. ANS: D PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two TrianglesOBJ: 5-7.1 To apply inequalities in two triangles NAT: CC G.CO.10| G.3.cTOP: 5-7 Problem 1 Using the Hinge Theorem

32. ANS: C PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two TrianglesOBJ: 5-7.1 To apply inequalities in two triangles NAT: CC G.CO.10| G.3.cTOP: 5-7 Problem 1 Using the Hinge Theorem

33. ANS: C PTS: 1 DIF: L2 REF: 5-7 Inequalities in Two TrianglesOBJ: 5-7.1 To apply inequalities in two triangles NAT: CC G.CO.10| G.3.cTOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem

34. ANS: D PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two TrianglesOBJ: 5-7.1 To apply inequalities in two triangles NAT: CC G.CO.10| G.3.cTOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem

ID: A

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35. ANS: BD AE, DF AC, BF CE

PTS: 1 DIF: L2 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.cTOP: 5-1 Problem 1 Identifying Parallel Segments KEY: midsegment | parallel lines | Triangle Midsegment Theorem