Ch 5 TEST 5.1-5.5, no 5 - Mrs. Woessner's Math...

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Name _________________________________________________________________________________Date _______ Period_______ Chapter 5 Review A 1 1. _________ 2. _________ 3. _________ Δ is isosceles with vertex angle A. 4. _________ 5. _________ 6. _________ 7. __________ 8. __________ 9. __________ 10. _________ What is the length of ? In Δ, is the centroid, = 18, and = 5. Find each length. The measures of two sides of a triangle are 10 meters and 23 meters. If the measure of the third side is meters, find the range of possible values of . Name the longest side of ABC. F −− AB F −− AB G −−− BC H −− AC J cannot tell Name the angle with greatest measure in DEF. A D C F A D B E C F D cannot tell Find the value of x. A 9 B 11 C 27 D 32 Find the shortest segment. Which of the following sets of numbers can be the lengths of the sides of a triangle? A 6, 6, 12 B 6, 7, 13 C 2 , 5, 15 D 2.6, 8.1, 10 A 6, 6, 12 B 6, 7, 13 C 2, 5, 15 D 2.6, 8.1, 10.2 If BD bisects ABC, find the value of x. 22° 84° 74° A C B x + 2 x + 7 A B C D E F 27 3 7 9 F D E 2x + 30 3x - 4 B C A D

Transcript of Ch 5 TEST 5.1-5.5, no 5 - Mrs. Woessner's Math...

Page 1: Ch 5 TEST 5.1-5.5, no 5 - Mrs. Woessner's Math Classroomawoessner.weebly.com/uploads/4/8/1/0/48104145/ch_5_review.pdfChapter 5 Glencoe Geometry 5 Chapter 5 Test, Form 2A SCORE Write

Name_________________________________________________________________________________Date_______Period_______Chapter5Review

A

1

1._________

2._________

3._________ Δ𝐴𝐸𝐶isisosceleswithvertexangleA.

4._________

5._________

6._________7.__________8.__________9.__________10._________

Whatisthelengthof𝐴𝐶?

InΔ𝑅𝑆𝑇,𝑍isthecentroid,𝑅𝑍 = 18,and𝑈𝑍 = 5.Findeachlength.𝑍𝑉𝑆𝑈Themeasuresoftwosidesofatriangleare10metersand23meters.Ifthemeasureofthethirdsideis𝑥meters,findtherangeofpossiblevaluesof𝑥.

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PDF 2nd

Chapter 5 51 Glencoe Geometry

5 SCORE Chapter 5 Test, Form 2A

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–4, refer to the figure. 1. Name an angle bisector. A −−

KI B ""# GL C $ ""# JM D −−− HJ

2. Name a median. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

3. Name an altitude. A −−

KI B ""# GL C $ ""# JM D −−−

HJ

4. Name a perpendicular bisector. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

For Questions 5–7, refer to the figure to determine which is a true statement for the given information. 5. −−−

YW is an angle bisector. A ∠YWZ is a right angle. C XW = WZ B ∠XYW & ∠ZYW D XY = ZY

6. −−− YW is an altitude.

F ∠YWZ is a right angle. H XW = WZ G ∠ XYW & ∠ZYW J XY = ZY

7. −−− YW is a median.

A ∠YWZ is a right angle. C XW = WZ B ∠ XYW & ∠ZYW D XY = ZY

8. Name the longest side of △ABC. F −−

AB H −− AC

G −−− BC J cannot tell

9. Name the angle with greatest measure in △DEF. A ∠D C ∠F B ∠E D cannot tell

10. Which theorem compares the sides of the same triangle? F Hinge Theorem H Exterior Angle Inequality Theorem G Converse of the Hinge Theorem J Triangle Inequality Theorem

11. Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

A corner between fences A and B B all three corners have the same measure C corner between the back of the house and fence A D corner between the back of the house and fence B

3

79

F

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22° 84°

74°

A C

B

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Z

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2.

3.

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6.

7.

8.

9.

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NAME DATE PERIOD

PDF 2nd

Chapter 5 51 Glencoe Geometry

5 SCORE Chapter 5 Test, Form 2A

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–4, refer to the figure. 1. Name an angle bisector. A −−

KI B ""# GL C $ ""# JM D −−− HJ

2. Name a median. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

3. Name an altitude. A −−

KI B ""# GL C $ ""# JM D −−−

HJ

4. Name a perpendicular bisector. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

For Questions 5–7, refer to the figure to determine which is a true statement for the given information. 5. −−−

YW is an angle bisector. A ∠YWZ is a right angle. C XW = WZ B ∠XYW & ∠ZYW D XY = ZY

6. −−− YW is an altitude.

F ∠YWZ is a right angle. H XW = WZ G ∠ XYW & ∠ZYW J XY = ZY

7. −−− YW is a median.

A ∠YWZ is a right angle. C XW = WZ B ∠ XYW & ∠ZYW D XY = ZY

8. Name the longest side of △ABC. F −−

AB H −− AC

G −−− BC J cannot tell

9. Name the angle with greatest measure in △DEF. A ∠D C ∠F B ∠E D cannot tell

10. Which theorem compares the sides of the same triangle? F Hinge Theorem H Exterior Angle Inequality Theorem G Converse of the Hinge Theorem J Triangle Inequality Theorem

11. Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

A corner between fences A and B B all three corners have the same measure C corner between the back of the house and fence A D corner between the back of the house and fence B

3

79

F

DE

22° 84°

74°

A C

B

XY

Z

W

H

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MI G

L K 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

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NAME DATE PERIOD

PDF 2nd

Chapter 5 51 Glencoe Geometry

5 SCORE Chapter 5 Test, Form 2A

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–4, refer to the figure. 1. Name an angle bisector. A −−

KI B ""# GL C $ ""# JM D −−− HJ

2. Name a median. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

3. Name an altitude. A −−

KI B ""# GL C $ ""# JM D −−−

HJ

4. Name a perpendicular bisector. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

For Questions 5–7, refer to the figure to determine which is a true statement for the given information. 5. −−−

YW is an angle bisector. A ∠YWZ is a right angle. C XW = WZ B ∠XYW & ∠ZYW D XY = ZY

6. −−− YW is an altitude.

F ∠YWZ is a right angle. H XW = WZ G ∠ XYW & ∠ZYW J XY = ZY

7. −−− YW is a median.

A ∠YWZ is a right angle. C XW = WZ B ∠ XYW & ∠ZYW D XY = ZY

8. Name the longest side of △ABC. F −−

AB H −− AC

G −−− BC J cannot tell

9. Name the angle with greatest measure in △DEF. A ∠D C ∠F B ∠E D cannot tell

10. Which theorem compares the sides of the same triangle? F Hinge Theorem H Exterior Angle Inequality Theorem G Converse of the Hinge Theorem J Triangle Inequality Theorem

11. Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

A corner between fences A and B B all three corners have the same measure C corner between the back of the house and fence A D corner between the back of the house and fence B

3

79

F

DE

22° 84°

74°

A C

B

XY

Z

W

H

J

MI G

L K 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

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NAME DATE PERIOD

PDF 2nd

Chapter 5 51 Glencoe Geometry

5 SCORE Chapter 5 Test, Form 2A

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–4, refer to the figure. 1. Name an angle bisector. A −−

KI B ""# GL C $ ""# JM D −−− HJ

2. Name a median. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

3. Name an altitude. A −−

KI B ""# GL C $ ""# JM D −−−

HJ

4. Name a perpendicular bisector. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

For Questions 5–7, refer to the figure to determine which is a true statement for the given information. 5. −−−

YW is an angle bisector. A ∠YWZ is a right angle. C XW = WZ B ∠XYW & ∠ZYW D XY = ZY

6. −−− YW is an altitude.

F ∠YWZ is a right angle. H XW = WZ G ∠ XYW & ∠ZYW J XY = ZY

7. −−− YW is a median.

A ∠YWZ is a right angle. C XW = WZ B ∠ XYW & ∠ZYW D XY = ZY

8. Name the longest side of △ABC. F −−

AB H −− AC

G −−− BC J cannot tell

9. Name the angle with greatest measure in △DEF. A ∠D C ∠F B ∠E D cannot tell

10. Which theorem compares the sides of the same triangle? F Hinge Theorem H Exterior Angle Inequality Theorem G Converse of the Hinge Theorem J Triangle Inequality Theorem

11. Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

A corner between fences A and B B all three corners have the same measure C corner between the back of the house and fence A D corner between the back of the house and fence B

3

79

F

DE

22° 84°

74°

A C

B

XY

Z

W

H

J

MI G

L K 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

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NAME DATE PERIOD

PDF 2nd

Chapter 5 51 Glencoe Geometry

5 SCORE Chapter 5 Test, Form 2A

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–4, refer to the figure. 1. Name an angle bisector. A −−

KI B ""# GL C $ ""# JM D −−− HJ

2. Name a median. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

3. Name an altitude. A −−

KI B ""# GL C $ ""# JM D −−−

HJ

4. Name a perpendicular bisector. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

For Questions 5–7, refer to the figure to determine which is a true statement for the given information. 5. −−−

YW is an angle bisector. A ∠YWZ is a right angle. C XW = WZ B ∠XYW & ∠ZYW D XY = ZY

6. −−− YW is an altitude.

F ∠YWZ is a right angle. H XW = WZ G ∠ XYW & ∠ZYW J XY = ZY

7. −−− YW is a median.

A ∠YWZ is a right angle. C XW = WZ B ∠ XYW & ∠ZYW D XY = ZY

8. Name the longest side of △ABC. F −−

AB H −− AC

G −−− BC J cannot tell

9. Name the angle with greatest measure in △DEF. A ∠D C ∠F B ∠E D cannot tell

10. Which theorem compares the sides of the same triangle? F Hinge Theorem H Exterior Angle Inequality Theorem G Converse of the Hinge Theorem J Triangle Inequality Theorem

11. Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

A corner between fences A and B B all three corners have the same measure C corner between the back of the house and fence A D corner between the back of the house and fence B

3

79

F

DE

22° 84°

74°

A C

B

XY

Z

W

H

J

MI G

L K 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

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NAME DATE PERIOD

PDF 2nd

Chapter 5 51 Glencoe Geometry

5 SCORE Chapter 5 Test, Form 2A

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–4, refer to the figure. 1. Name an angle bisector. A −−

KI B ""# GL C $ ""# JM D −−− HJ

2. Name a median. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

3. Name an altitude. A −−

KI B ""# GL C $ ""# JM D −−−

HJ

4. Name a perpendicular bisector. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

For Questions 5–7, refer to the figure to determine which is a true statement for the given information. 5. −−−

YW is an angle bisector. A ∠YWZ is a right angle. C XW = WZ B ∠XYW & ∠ZYW D XY = ZY

6. −−− YW is an altitude.

F ∠YWZ is a right angle. H XW = WZ G ∠ XYW & ∠ZYW J XY = ZY

7. −−− YW is a median.

A ∠YWZ is a right angle. C XW = WZ B ∠ XYW & ∠ZYW D XY = ZY

8. Name the longest side of △ABC. F −−

AB H −− AC

G −−− BC J cannot tell

9. Name the angle with greatest measure in △DEF. A ∠D C ∠F B ∠E D cannot tell

10. Which theorem compares the sides of the same triangle? F Hinge Theorem H Exterior Angle Inequality Theorem G Converse of the Hinge Theorem J Triangle Inequality Theorem

11. Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

A corner between fences A and B B all three corners have the same measure C corner between the back of the house and fence A D corner between the back of the house and fence B

3

79

F

DE

22° 84°

74°

A C

B

XY

Z

W

H

J

MI G

L K 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

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PDF 2nd

Chapter 5 52 Glencoe Geometry

5

12. Find the possible values for m∠1. F 90 > m∠1 > 74 H 0 < m∠1 < 74 G 180 > m∠1 > 74 J m∠1 = 106

13. Find the value of x. A 9 C 27 B 11 D 32

14. Which is another name for an indirect proof? F proof by deduction H proof by inverse G proof by converse J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2. A x > 2 B x ≥ 2 C x = 2 D x ≤ 2

16. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: m∠1 = m∠B + m∠C F ∠1 is not an exterior angle of △ABC. G ∠1 is an interior angle of △ABC. H m∠1 ≠ m∠B + m∠C J m∠1 = m∠B

17. Which of the following sets of numbers can be the lengths of the sides of a triangle?

A 6, 6, 12 B 6, 7, 13 C √ ' 2 , √ ' 5 , √ '' 15 D 2.6, 8.1, 10.2

18. What is the relationship between the lengths of −−−

QS and

−− RS ?

F QS = RS H QS > RS G QS < RS J cannot tell

19. What is the relationship between the lengths of −−−

DC and

−−− AD ?

A DC < AD C DC = AD B DC > AD D cannot tell

20. What is the relationship between the measures of ∠1 and ∠2?

F m∠1 = m∠2 H m∠1 > m∠2 G m∠1 < m∠2 J cannot tell

Bonus −−− YW bisects ∠XYZ in △XYZ. Point W is on −−

XZ . If m∠XYW = 2x + 18 and m∠ZYW = x2 - 5x, find the possible value(s) of x.

8

8

15

131

2

10

10

30°20°

A

C

D

B

RT

Q S

12.

13.

14.

15.

16.

17.

18.

19.

20.

x + 2

x + 7A

BC

D

EF27

174°

Chapter 5 Test, Form 2A (continued)

B:

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PDF 2nd

Chapter 5 52 Glencoe Geometry

5

12. Find the possible values for m∠1. F 90 > m∠1 > 74 H 0 < m∠1 < 74 G 180 > m∠1 > 74 J m∠1 = 106

13. Find the value of x. A 9 C 27 B 11 D 32

14. Which is another name for an indirect proof? F proof by deduction H proof by inverse G proof by converse J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2. A x > 2 B x ≥ 2 C x = 2 D x ≤ 2

16. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: m∠1 = m∠B + m∠C F ∠1 is not an exterior angle of △ABC. G ∠1 is an interior angle of △ABC. H m∠1 ≠ m∠B + m∠C J m∠1 = m∠B

17. Which of the following sets of numbers can be the lengths of the sides of a triangle?

A 6, 6, 12 B 6, 7, 13 C √ ' 2 , √ ' 5 , √ '' 15 D 2.6, 8.1, 10.2

18. What is the relationship between the lengths of −−−

QS and

−− RS ?

F QS = RS H QS > RS G QS < RS J cannot tell

19. What is the relationship between the lengths of −−−

DC and

−−− AD ?

A DC < AD C DC = AD B DC > AD D cannot tell

20. What is the relationship between the measures of ∠1 and ∠2?

F m∠1 = m∠2 H m∠1 > m∠2 G m∠1 < m∠2 J cannot tell

Bonus −−− YW bisects ∠XYZ in △XYZ. Point W is on −−

XZ . If m∠XYW = 2x + 18 and m∠ZYW = x2 - 5x, find the possible value(s) of x.

8

8

15

131

2

10

10

30°20°

A

C

D

B

RT

Q S

12.

13.

14.

15.

16.

17.

18.

19.

20.

x + 2

x + 7A

BC

D

EF27

174°

Chapter 5 Test, Form 2A (continued)

B:

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NAME DATE PERIOD

PDF 2nd

5 SCORE Chapter 5 Test, Form 2C

1. Name an angle bisector.

2. The perimeter of ABCD is 44. Find the value of x. Then describe the relationship between ! "# AC and −−−

BD .

3. If point E is the centroid of △ABC, BD = 12, EF = 7, and AG = 15, find ED.

4. The vertices of △XYZ are X(-2, 6), Y(4, 10), and Z(14, 6). Find the coordinates of the centroid of △XYZ.

5. If −−− PO is an angle bisector of ∠MON,

find the value of x.

6. A biker will jump over a ramp, where x and z are measured in feet. Write an inequality relating x and z.

7. List the angles of △GHI in order from smallest to largest measure.

8. List the sides of △PQR in order from shortest to longest.

9. Find the shortest segment.

10. Write the assumption you would make to start an indirect proof of the statement. If 16 is a factor of n, then 4 is a factor of n.

11. Write the assumption you would make to start an indirect proof of the statement. If

−− AB is an altitude of equilateral

triangle ABC, then −−

AB is a median.

2(z + 3)x5165˚

70˚

55°55°65°

65˚60°

60°

Y

X Z

W

80° 45°

55°

Q

P R

2 in.1.2 in.

3 in.

IG

H

(2x - 10)° (x + 15)°O

PN M

DA C

B

F G

E

2x - 3

2x - 7x + 5

x + 1

D

B

AC

G

B CD

A

E

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2.

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Chapter 5 55 Glencoe Geometry

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PDF 2nd

Chapter 5 52 Glencoe Geometry

5

12. Find the possible values for m∠1. F 90 > m∠1 > 74 H 0 < m∠1 < 74 G 180 > m∠1 > 74 J m∠1 = 106

13. Find the value of x. A 9 C 27 B 11 D 32

14. Which is another name for an indirect proof? F proof by deduction H proof by inverse G proof by converse J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2. A x > 2 B x ≥ 2 C x = 2 D x ≤ 2

16. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: m∠1 = m∠B + m∠C F ∠1 is not an exterior angle of △ABC. G ∠1 is an interior angle of △ABC. H m∠1 ≠ m∠B + m∠C J m∠1 = m∠B

17. Which of the following sets of numbers can be the lengths of the sides of a triangle?

A 6, 6, 12 B 6, 7, 13 C √ ' 2 , √ ' 5 , √ '' 15 D 2.6, 8.1, 10.2

18. What is the relationship between the lengths of −−−

QS and

−− RS ?

F QS = RS H QS > RS G QS < RS J cannot tell

19. What is the relationship between the lengths of −−−

DC and

−−− AD ?

A DC < AD C DC = AD B DC > AD D cannot tell

20. What is the relationship between the measures of ∠1 and ∠2?

F m∠1 = m∠2 H m∠1 > m∠2 G m∠1 < m∠2 J cannot tell

Bonus −−− YW bisects ∠XYZ in △XYZ. Point W is on −−

XZ . If m∠XYW = 2x + 18 and m∠ZYW = x2 - 5x, find the possible value(s) of x.

8

8

15

131

2

10

10

30°20°

A

C

D

B

RT

Q S

12.

13.

14.

15.

16.

17.

18.

19.

20.

x + 2

x + 7A

BC

D

EF27

174°

Chapter 5 Test, Form 2A (continued)

B:

044_053_GEOCRMC05_890514.indd 52044_053_GEOCRMC05_890514.indd 52 6/19/08 5:25:11 PM6/19/08 5:25:11 PM

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PDF 2nd

Chapter 5 52 Glencoe Geometry

5

12. Find the possible values for m∠1. F 90 > m∠1 > 74 H 0 < m∠1 < 74 G 180 > m∠1 > 74 J m∠1 = 106

13. Find the value of x. A 9 C 27 B 11 D 32

14. Which is another name for an indirect proof? F proof by deduction H proof by inverse G proof by converse J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2. A x > 2 B x ≥ 2 C x = 2 D x ≤ 2

16. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: m∠1 = m∠B + m∠C F ∠1 is not an exterior angle of △ABC. G ∠1 is an interior angle of △ABC. H m∠1 ≠ m∠B + m∠C J m∠1 = m∠B

17. Which of the following sets of numbers can be the lengths of the sides of a triangle?

A 6, 6, 12 B 6, 7, 13 C √ ' 2 , √ ' 5 , √ '' 15 D 2.6, 8.1, 10.2

18. What is the relationship between the lengths of −−−

QS and

−− RS ?

F QS = RS H QS > RS G QS < RS J cannot tell

19. What is the relationship between the lengths of −−−

DC and

−−− AD ?

A DC < AD C DC = AD B DC > AD D cannot tell

20. What is the relationship between the measures of ∠1 and ∠2?

F m∠1 = m∠2 H m∠1 > m∠2 G m∠1 < m∠2 J cannot tell

Bonus −−− YW bisects ∠XYZ in △XYZ. Point W is on −−

XZ . If m∠XYW = 2x + 18 and m∠ZYW = x2 - 5x, find the possible value(s) of x.

8

8

15

131

2

10

10

30°20°

A

C

D

B

RT

Q S

12.

13.

14.

15.

16.

17.

18.

19.

20.

x + 2

x + 7A

BC

D

EF27

174°

Chapter 5 Test, Form 2A (continued)

B:

044_053_GEOCRMC05_890514.indd 52044_053_GEOCRMC05_890514.indd 52 6/19/08 5:25:11 PM6/19/08 5:25:11 PM

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yright © G

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ill, a division of The M

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PDF 2nd

Chapter 5 52 Glencoe Geometry

5

12. Find the possible values for m∠1. F 90 > m∠1 > 74 H 0 < m∠1 < 74 G 180 > m∠1 > 74 J m∠1 = 106

13. Find the value of x. A 9 C 27 B 11 D 32

14. Which is another name for an indirect proof? F proof by deduction H proof by inverse G proof by converse J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2. A x > 2 B x ≥ 2 C x = 2 D x ≤ 2

16. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: m∠1 = m∠B + m∠C F ∠1 is not an exterior angle of △ABC. G ∠1 is an interior angle of △ABC. H m∠1 ≠ m∠B + m∠C J m∠1 = m∠B

17. Which of the following sets of numbers can be the lengths of the sides of a triangle?

A 6, 6, 12 B 6, 7, 13 C √ ' 2 , √ ' 5 , √ '' 15 D 2.6, 8.1, 10.2

18. What is the relationship between the lengths of −−−

QS and

−− RS ?

F QS = RS H QS > RS G QS < RS J cannot tell

19. What is the relationship between the lengths of −−−

DC and

−−− AD ?

A DC < AD C DC = AD B DC > AD D cannot tell

20. What is the relationship between the measures of ∠1 and ∠2?

F m∠1 = m∠2 H m∠1 > m∠2 G m∠1 < m∠2 J cannot tell

Bonus −−− YW bisects ∠XYZ in △XYZ. Point W is on −−

XZ . If m∠XYW = 2x + 18 and m∠ZYW = x2 - 5x, find the possible value(s) of x.

8

8

15

131

2

10

10

30°20°

A

C

D

B

RT

Q S

12.

13.

14.

15.

16.

17.

18.

19.

20.

x + 2

x + 7A

BC

D

EF27

174°

Chapter 5 Test, Form 2A (continued)

B:

044_053_GEOCRMC05_890514.indd 52044_053_GEOCRMC05_890514.indd 52 6/19/08 5:25:11 PM6/19/08 5:25:11 PM

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PDF 2nd

Chapter 5 52 Glencoe Geometry

5

12. Find the possible values for m∠1. F 90 > m∠1 > 74 H 0 < m∠1 < 74 G 180 > m∠1 > 74 J m∠1 = 106

13. Find the value of x. A 9 C 27 B 11 D 32

14. Which is another name for an indirect proof? F proof by deduction H proof by inverse G proof by converse J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2. A x > 2 B x ≥ 2 C x = 2 D x ≤ 2

16. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: m∠1 = m∠B + m∠C F ∠1 is not an exterior angle of △ABC. G ∠1 is an interior angle of △ABC. H m∠1 ≠ m∠B + m∠C J m∠1 = m∠B

17. Which of the following sets of numbers can be the lengths of the sides of a triangle?

A 6, 6, 12 B 6, 7, 13 C √ ' 2 , √ ' 5 , √ '' 15 D 2.6, 8.1, 10.2

18. What is the relationship between the lengths of −−−

QS and

−− RS ?

F QS = RS H QS > RS G QS < RS J cannot tell

19. What is the relationship between the lengths of −−−

DC and

−−− AD ?

A DC < AD C DC = AD B DC > AD D cannot tell

20. What is the relationship between the measures of ∠1 and ∠2?

F m∠1 = m∠2 H m∠1 > m∠2 G m∠1 < m∠2 J cannot tell

Bonus −−− YW bisects ∠XYZ in △XYZ. Point W is on −−

XZ . If m∠XYW = 2x + 18 and m∠ZYW = x2 - 5x, find the possible value(s) of x.

8

8

15

131

2

10

10

30°20°

A

C

D

B

RT

Q S

12.

13.

14.

15.

16.

17.

18.

19.

20.

x + 2

x + 7A

BC

D

EF27

174°

Chapter 5 Test, Form 2A (continued)

B:

044_053_GEOCRMC05_890514.indd 52044_053_GEOCRMC05_890514.indd 52 6/19/08 5:25:11 PM6/19/08 5:25:11 PM

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PDF 2nd

Chapter 5 52 Glencoe Geometry

5

12. Find the possible values for m∠1. F 90 > m∠1 > 74 H 0 < m∠1 < 74 G 180 > m∠1 > 74 J m∠1 = 106

13. Find the value of x. A 9 C 27 B 11 D 32

14. Which is another name for an indirect proof? F proof by deduction H proof by inverse G proof by converse J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2. A x > 2 B x ≥ 2 C x = 2 D x ≤ 2

16. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: m∠1 = m∠B + m∠C F ∠1 is not an exterior angle of △ABC. G ∠1 is an interior angle of △ABC. H m∠1 ≠ m∠B + m∠C J m∠1 = m∠B

17. Which of the following sets of numbers can be the lengths of the sides of a triangle?

A 6, 6, 12 B 6, 7, 13 C √ ' 2 , √ ' 5 , √ '' 15 D 2.6, 8.1, 10.2

18. What is the relationship between the lengths of −−−

QS and

−− RS ?

F QS = RS H QS > RS G QS < RS J cannot tell

19. What is the relationship between the lengths of −−−

DC and

−−− AD ?

A DC < AD C DC = AD B DC > AD D cannot tell

20. What is the relationship between the measures of ∠1 and ∠2?

F m∠1 = m∠2 H m∠1 > m∠2 G m∠1 < m∠2 J cannot tell

Bonus −−− YW bisects ∠XYZ in △XYZ. Point W is on −−

XZ . If m∠XYW = 2x + 18 and m∠ZYW = x2 - 5x, find the possible value(s) of x.

8

8

15

131

2

10

10

30°20°

A

C

D

B

RT

Q S

12.

13.

14.

15.

16.

17.

18.

19.

20.

x + 2

x + 7A

BC

D

EF27

174°

Chapter 5 Test, Form 2A (continued)

B:

044_053_GEOCRMC05_890514.indd 52044_053_GEOCRMC05_890514.indd 52 6/19/08 5:25:11 PM6/19/08 5:25:11 PM

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PDF 2nd

5

C

BA D

5 ft

5 ft

12 ft

11 ft1

2

R Q

P

S T U

Y

ZX W 12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

12. Write the assumption you would make to start an indirect proof for the following.

Given: −− XY " −−

YZ −−−

YW bisects ∠XYZ. Prove: ∠X " ∠Z

13. The measures of two sides of a triangle are 10 meters and 23 meters. If the measure of the third side is x meters, find the range for the value of x.

14. −−− PU is a median of △PTQ.

If UQ = 6, find TQ.

15. If %%& BD bisects ∠ABC, find the value of x.

16. Write an inequality to compare EF and GH.

17. Write an inequality to compare m∠1 and m∠2.

For Questions 18–20, complete the proof below by supplying the missing information for each corresponding location.Given: AD = CB and AC > DBProve: m∠ ADC > m∠DCB

Proof:Statements Reasons

1. AD = CB and AC > DB 1. Given

2. −−−

AD ' −−− CB 2. (Question 18)

3. −−− CD ' −−−

CD 3. (Question 19)

4. m∠ADC > m∠DCB 4. (Question 20)

Bonus Write an equation in slope-intercept form for the altitude to

−−− BC .

x

y

C(2c, 0)A(0, 0)

B(2a, 2b)

O

2x + 30

3x - 4B C

A

D

Chapter 5 56 Glencoe Geometry

Chapter 5 Test, Form 2C (continued)

23°20°

H

G F

E

6

6

054_064_GEOCRMC05_890514.indd 56054_064_GEOCRMC05_890514.indd 56 6/12/08 12:37:22 AM6/12/08 12:37:22 AM

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smen

t

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a d

ivis

ion

of T

he M

cGra

w-H

ill C

ompa

nies

, Inc

.

NAME DATE PERIOD

PDF 2nd

Chapter 5 51 Glencoe Geometry

5 SCORE Chapter 5 Test, Form 2A

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–4, refer to the figure. 1. Name an angle bisector. A −−

KI B ""# GL C $ ""# JM D −−− HJ

2. Name a median. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

3. Name an altitude. A −−

KI B ""# GL C $ ""# JM D −−−

HJ

4. Name a perpendicular bisector. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

For Questions 5–7, refer to the figure to determine which is a true statement for the given information. 5. −−−

YW is an angle bisector. A ∠YWZ is a right angle. C XW = WZ B ∠XYW & ∠ZYW D XY = ZY

6. −−− YW is an altitude.

F ∠YWZ is a right angle. H XW = WZ G ∠ XYW & ∠ZYW J XY = ZY

7. −−− YW is a median.

A ∠YWZ is a right angle. C XW = WZ B ∠ XYW & ∠ZYW D XY = ZY

8. Name the longest side of △ABC. F −−

AB H −− AC

G −−− BC J cannot tell

9. Name the angle with greatest measure in △DEF. A ∠D C ∠F B ∠E D cannot tell

10. Which theorem compares the sides of the same triangle? F Hinge Theorem H Exterior Angle Inequality Theorem G Converse of the Hinge Theorem J Triangle Inequality Theorem

11. Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

A corner between fences A and B B all three corners have the same measure C corner between the back of the house and fence A D corner between the back of the house and fence B

3

79

F

DE

22° 84°

74°

A C

B

XY

Z

W

H

J

MI G

L K 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

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cGraw

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ompanies, Inc.

NAME DATE PERIOD

PDF 2nd

Chapter 5 52 Glencoe Geometry

5

12. Find the possible values for m∠1. F 90 > m∠1 > 74 H 0 < m∠1 < 74 G 180 > m∠1 > 74 J m∠1 = 106

13. Find the value of x. A 9 C 27 B 11 D 32

14. Which is another name for an indirect proof? F proof by deduction H proof by inverse G proof by converse J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2. A x > 2 B x ≥ 2 C x = 2 D x ≤ 2

16. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: m∠1 = m∠B + m∠C F ∠1 is not an exterior angle of △ABC. G ∠1 is an interior angle of △ABC. H m∠1 ≠ m∠B + m∠C J m∠1 = m∠B

17. Which of the following sets of numbers can be the lengths of the sides of a triangle?

A 6, 6, 12 B 6, 7, 13 C √ ' 2 , √ ' 5 , √ '' 15 D 2.6, 8.1, 10.2

18. What is the relationship between the lengths of −−−

QS and

−− RS ?

F QS = RS H QS > RS G QS < RS J cannot tell

19. What is the relationship between the lengths of −−−

DC and

−−− AD ?

A DC < AD C DC = AD B DC > AD D cannot tell

20. What is the relationship between the measures of ∠1 and ∠2?

F m∠1 = m∠2 H m∠1 > m∠2 G m∠1 < m∠2 J cannot tell

Bonus −−− YW bisects ∠XYZ in △XYZ. Point W is on −−

XZ . If m∠XYW = 2x + 18 and m∠ZYW = x2 - 5x, find the possible value(s) of x.

8

8

15

131

2

10

10

30°20°

A

C

D

B

RT

Q S

12.

13.

14.

15.

16.

17.

18.

19.

20.

x + 2

x + 7A

BC

D

EF27

174°

Chapter 5 Test, Form 2A (continued)

B:

044_053_GEOCRMC05_890514.indd 52044_053_GEOCRMC05_890514.indd 52 6/19/08 5:25:11 PM6/19/08 5:25:11 PM

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ent

Cop

yrig

ht ©

Gle

ncoe

/McG

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-Hill

, a d

ivis

ion

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he M

cGra

w-H

ill C

ompa

nies

, Inc

.

NAME DATE PERIOD

PDF 2nd

Chapter 5 51 Glencoe Geometry

5 SCORE Chapter 5 Test, Form 2A

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–4, refer to the figure. 1. Name an angle bisector. A −−

KI B ""# GL C $ ""# JM D −−− HJ

2. Name a median. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

3. Name an altitude. A −−

KI B ""# GL C $ ""# JM D −−−

HJ

4. Name a perpendicular bisector. F −−

KI G ""# GL H $ ""# JM J −−−

HJ

For Questions 5–7, refer to the figure to determine which is a true statement for the given information. 5. −−−

YW is an angle bisector. A ∠YWZ is a right angle. C XW = WZ B ∠XYW & ∠ZYW D XY = ZY

6. −−− YW is an altitude.

F ∠YWZ is a right angle. H XW = WZ G ∠ XYW & ∠ZYW J XY = ZY

7. −−− YW is a median.

A ∠YWZ is a right angle. C XW = WZ B ∠ XYW & ∠ZYW D XY = ZY

8. Name the longest side of △ABC. F −−

AB H −− AC

G −−− BC J cannot tell

9. Name the angle with greatest measure in △DEF. A ∠D C ∠F B ∠E D cannot tell

10. Which theorem compares the sides of the same triangle? F Hinge Theorem H Exterior Angle Inequality Theorem G Converse of the Hinge Theorem J Triangle Inequality Theorem

11. Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

A corner between fences A and B B all three corners have the same measure C corner between the back of the house and fence A D corner between the back of the house and fence B

3

79

F

DE

22° 84°

74°

A C

B

XY

Z

W

H

J

MI G

L K 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

044_053_GEOCRMC05_890514.indd 51044_053_GEOCRMC05_890514.indd 51 6/19/08 5:25:07 PM6/19/08 5:25:07 PM

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cGraw

-Hill, a division of The M

cGraw

-Hill C

ompanies, Inc.

NAME DATE PERIOD

PDF 2nd

5

C

BA D

5 ft

5 ft

12 ft

11 ft1

2

R Q

P

S T U

Y

ZX W 12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

12. Write the assumption you would make to start an indirect proof for the following.

Given: −− XY " −−

YZ −−−

YW bisects ∠XYZ. Prove: ∠X " ∠Z

13. The measures of two sides of a triangle are 10 meters and 23 meters. If the measure of the third side is x meters, find the range for the value of x.

14. −−− PU is a median of △PTQ.

If UQ = 6, find TQ.

15. If %%& BD bisects ∠ABC, find the value of x.

16. Write an inequality to compare EF and GH.

17. Write an inequality to compare m∠1 and m∠2.

For Questions 18–20, complete the proof below by supplying the missing information for each corresponding location.Given: AD = CB and AC > DBProve: m∠ ADC > m∠DCB

Proof:Statements Reasons

1. AD = CB and AC > DB 1. Given

2. −−−

AD ' −−− CB 2. (Question 18)

3. −−− CD ' −−−

CD 3. (Question 19)

4. m∠ADC > m∠DCB 4. (Question 20)

Bonus Write an equation in slope-intercept form for the altitude to

−−− BC .

x

y

C(2c, 0)A(0, 0)

B(2a, 2b)

O

2x + 30

3x - 4B C

A

D

Chapter 5 56 Glencoe Geometry

Chapter 5 Test, Form 2C (continued)

23°20°

H

G F

E

6

6

054_064_GEOCRMC05_890514.indd 56054_064_GEOCRMC05_890514.indd 56 6/12/08 12:37:22 AM6/12/08 12:37:22 AM