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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Geometry

Foundations for Geometry Chapter Test Form A

Circle the best answer.

Use the figure for Exercises 1–4.

1. What is another name for plane P ?

A plane B C plane ABC B plane n D plane BAD

2. Which segment is on line n?

A DA

B BC

3. Which is the name of a ray with endpoint B?

A ABJJJG

C DB

B BCHJJG

D BAJJJG

4. Name the intersection of line n and AC . A point B B point C

5. F is between E and G, EF 7, and FG 6. Find EG. A 6 C 13 B 7 D 26

6. LM QP and LM 12. Find QP.

A 6 B 12

7. Which term describes LMP?

A acute B obtuse

8. What is m WXY?

A 20 C 60 B 40 D 100

9. Which pair of angles is adjacent?

A 1 and 2 B 1 and 3

10. If m A 47 , what is the measure of a complement of A? A 43 B 133

Chapter

x

7

Chapter

1

7

CS10_G_MEAR710334_C01MCCT.indd 7 405011 11:57:04 AM



Answer Key Foundations for Geometry

Section Quiz: Lessons 1-1 Through 1-4

1. C 8. F 2. G 9. A 3. B 10. J 4. J 11. A 5. C 12. G 6. J 13. B 7. B


1. D 5. D 2. H 6. H 3. C 7. B 4. F 8. G

Chapter Test Form A: Multiple Choice

1. C 11. D 2. B 12. A 3. D 13. A 4. B 14. C 5. C 15. B 6. B 16. B 7. A 17. A 8. D 18. A 9. A 19. A 10. A 20. A

Chapter Test Form B: Multiple Choice

1. C 11. B 2. F 12. G 3. D 13. A 4. G 14. H 5. D 15. B 6. J 16. J 7. C 17. C 8. J 18. F 9. D 19. B 10. J 20. J

Chapter Test Form C: Multiple Choice

1. D 11. B

2. G 12. G

3. D 13. D

4. F 14. F

5. C 15. A

6. F 16. H

7. D 17. C

8. G 18. G

9. B 19. A

10. H 20. F

Chapter Test Form A: Free Response

1. Possible answers: HJJG HJJG

, ,BC CB or line n

2. BC or CB

3. JJJGAD

4. point B

5. 28 units

6. 9 units

7. acute

8. 130

9. Possible answers: 1 and 5, or 4 and 5

10. 61

11. 43

12. 28 cm

13. 24 in2

14. 18 ft

15. ( 5, 6)

16. (14, 6)

17. 41 units

18. 5 cm

19. translation

20. A (1, 1), B (5, 1)

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CS10_G_MEAR710334_C01AK.indd 243 405011 11:55:03 AM





1. C 8. F 2. G 9. A 3. B 10. J 4. J 11. A 5. C 12. G 6. J 13. B 7. B


1. D 5. D 2. H 6. H 3. C 7. B 4. F 8. G






1. D 11. B

2. G 12. G

3. D 13. D

4. F 14. F

5. C 15. A

6. F 16. H

7. D 17. C

8. G 18. G

9. B 19. A

10. H 20. F



, ,BC CB or line n

2. BC or CB

3. JJJGAD

4. point B

5. 28 units

6. 9 units

7. acute

8. 130


10. 61

11. 43

12. 28 cm

13. 24 in2

14. 18 ft

15. ( 5, 6)

16. (14, 6)

17. 41 units

18. 5 cm

19. translation

20. A (1, 1), B (5, 1)

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Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form C



1. Which is a name for the plane containing

point D?

A plane DB C plane EBD

B plane P D plane FDE

2. Which segment is on plane P but is NOT on line n?

F BE H BC

G GB J AC

3. Which names a pair of opposite rays?

A ABJJJG

and BGJJJG

C ABJJJG

and BAJJJG

B BCJJJG

and ABJJJG

D BDJJJG

and BEJJJG

4. Name the intersection of the two planes.

F line n H line m

G point B J AC

5. R, S, and T are collinear, and S is between R and T. If RS x 1, ST 2x 2, and RT 5x 5, find RT.

A 2 C 5

B 3 D 6

6. Given LM MP, which of the following is always true?

F LM MP

G M is the midpoint of .LP

H M bisects .LP

J L, M, and P are collinear.

7. Find m LMQ.

A 68 C 112

B 90 D 158

8. XZJJJG

bisects WXY, and m WXY 180 . What is m ZXY?

F 45 H 135

G 90 J 180

9. Which angles are adjacent but do NOT form a linear pair?

A 1 and 5 C 2 and 4

B 2 and 3 D 4 and 5

Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form B continued

11. If m B (3x 16) , what is the measure of the supplement of B? A 180 C (164 3x) B (196 3x) D (16 3x)

12. What is the perimeter of a square whose side is 8.2 centimeters? F 16.4 cm H 32.8 cm2 G 32.8 cm J 67.24 cm2

13. What is the area of a triangle with a height of 3 inches and a base of 5.5 inches? A 8.25 in2 C 16.5 in. B 8.5 in2 D 16.5 in2

14. A circle has a diameter of 8 feet. What is its approximate area? F 12.56 ft2 H 50.24 ft2 G 25.12 ft2 J 200.96 ft2

15. Given GH with endpoints G( 11, 4) and H( 1, 9), what are the coordinates of the midpoint of GH ? A ( 12, 5) C ( 10, 13) B ( 6, 2.5) D ( 5, 6.5)

16. M is the midpoint of .RS R has coordinates ( 12, 4), and M has coordinates (1, 2). What are the coordinates of S? F ( 5.5, 1) H (13, 6) G ( 11, 2) J (14, 8)

17. What is the distance from M( 1, 6) to N(11, 1)? A 12 units C 13 units

B 149 units D 169 units

18. What is the distance from V to W?

F 17 cm H 120 cm G 23 cm J 289 cm

19. What transformation is shown?

A rotation C translation B reflection D image

20. Given a point in the coordinate plane, the rule (x, y) (x 2, y 3) translates the point in which direction? F 2 units to the left and 3 units up G 3 units to the left and 2 units down H 3 units right and 2 units up J 2 units to the right and 3 units down

Chapter

x

10

Chapter

1

10






1. C 8. F 2. G 9. A 3. B 10. J 4. J 11. A 5. C 12. G 6. J 13. B 7. B


1. D 5. D 2. H 6. H 3. C 7. B 4. F 8. G






1. D 11. B

2. G 12. G

3. D 13. D

4. F 14. F

5. C 15. A

6. F 16. H

7. D 17. C

8. G 18. G

9. B 19. A

10. H 20. F



, ,BC CB or line n

2. BC or CB

3. JJJGAD

4. point B

5. 28 units

6. 9 units

7. acute

8. 130


10. 61

11. 43

12. 28 cm

13. 24 in2

14. 18 ft

15. ( 5, 6)

16. (14, 6)

17. 41 units

18. 5 cm

19. translation

20. A (1, 1), B (5, 1)

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Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form C



1. Which is a name for the plane containing

point D?

A plane DB C plane EBD

B plane P D plane FDE

2. Which segment is on plane P but is NOT on line n?

F BE H BC

G GB J AC

3. Which names a pair of opposite rays?

A ABJJJG

and BGJJJG

C ABJJJG

and BAJJJG

B BCJJJG

and ABJJJG

D BDJJJG

and BEJJJG

4. Name the intersection of the two planes.

F line n H line m

G point B J AC

5. R, S, and T are collinear, and S is between R and T. If RS x 1, ST 2x 2, and RT 5x 5, find RT.

A 2 C 5

B 3 D 6

6. Given LM MP, which of the following is always true?

F LM MP

G M is the midpoint of .LP

H M bisects .LP

J L, M, and P are collinear.

7. Find m LMQ.

A 68 C 112

B 90 D 158

8. XZJJJG

bisects WXY, and m WXY 180 . What is m ZXY?

F 45 H 135

G 90 J 180

9. Which angles are adjacent but do NOT form a linear pair?

A 1 and 5 C 2 and 4

B 2 and 3 D 4 and 5

Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form B continued

11. If m B (3x 16) , what is the measure of the supplement of B? A 180 C (164 3x) B (196 3x) D (16 3x)

12. What is the perimeter of a square whose side is 8.2 centimeters? F 16.4 cm H 32.8 cm2 G 32.8 cm J 67.24 cm2

13. What is the area of a triangle with a height of 3 inches and a base of 5.5 inches? A 8.25 in2 C 16.5 in. B 8.5 in2 D 16.5 in2

14. A circle has a diameter of 8 feet. What is its approximate area? F 12.56 ft2 H 50.24 ft2 G 25.12 ft2 J 200.96 ft2

15. Given GH with endpoints G( 11, 4) and H( 1, 9), what are the coordinates of the midpoint of GH ? A ( 12, 5) C ( 10, 13) B ( 6, 2.5) D ( 5, 6.5)

16. M is the midpoint of .RS R has coordinates ( 12, 4), and M has coordinates (1, 2). What are the coordinates of S? F ( 5.5, 1) H (13, 6) G ( 11, 2) J (14, 8)

17. What is the distance from M( 1, 6) to N(11, 1)? A 12 units C 13 units

B 149 units D 169 units

18. What is the distance from V to W?

F 17 cm H 120 cm G 23 cm J 289 cm

19. What transformation is shown?

A rotation C translation B reflection D image

20. Given a point in the coordinate plane, the rule (x, y) (x 2, y 3) translates the point in which direction? F 2 units to the left and 3 units up G 3 units to the left and 2 units down H 3 units right and 2 units up J 2 units to the right and 3 units down

Chapter

x

11

Chapter

1

11






1. C 8. F 2. G 9. A 3. B 10. J 4. J 11. A 5. C 12. G 6. J 13. B 7. B


1. D 5. D 2. H 6. H 3. C 7. B 4. F 8. G






1. D 11. B

2. G 12. G

3. D 13. D

4. F 14. F

5. C 15. A

6. F 16. H

7. D 17. C

8. G 18. G

9. B 19. A

10. H 20. F



, ,BC CB or line n

2. BC or CB

3. JJJGAD

4. point B

5. 28 units

6. 9 units

7. acute

8. 130


10. 61

11. 43

12. 28 cm

13. 24 in2

14. 18 ft

15. ( 5, 6)

16. (14, 6)

17. 41 units

18. 5 cm

19. translation

20. A (1, 1), B (5, 1)

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1. C 8. F 2. G 9. A 3. B 10. J 4. J 11. A 5. C 12. G 6. J 13. B 7. B


1. D 5. D 2. H 6. H 3. C 7. B 4. F 8. G






1. D 11. B

2. G 12. G

3. D 13. D

4. F 14. F

5. C 15. A

6. F 16. H

7. D 17. C

8. G 18. G

9. B 19. A

10. H 20. F



, ,BC CB or line n

2. BC or CB

3. JJJGAD

4. point B

5. 28 units

6. 9 units

7. acute

8. 130


10. 61

11. 43

12. 28 cm

13. 24 in2

14. 18 ft

15. ( 5, 6)

16. (14, 6)

17. 41 units

18. 5 cm

19. translation

20. A (1, 1), B (5, 1)

243243


Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Section A Quiz

Choose the best answer. Use this figure for Exercises 1 and 2.

1. What is the name of the

ray with endpoint is K and that passes through R?

A KSJJJG

C RKHJJG

B KTJJJG

2. In the diagram, how many different rays have endpoint R?

F 1 H 3

G 2

Use this figure for Exercises 3 and 4.

3. Which line contains points S and U?

A line m C line p

B line n

4. In the diagram, how many different segments can be named?

F 1 H 3

G 2

Use this figure for Exercises 5 and 6.

5. What is the length of MP?

A 2 C 5

B 4

6. What is the length of LP?

F 7.5 H 7.5

G 2.5

7. What is the first step in constructing a segment congruent to KL ?

A Measure KL . C Swing an arc B Draw a line with with compass straightedge. point on K.

8. B is the midpoint of AC . AB = 8v, and AC = 2v + 42. What is BC?

F 7 H 56

G 48

9. An angle whose measure is 70° is what type of angle?

A acute C obtuse

B right

10. GJJJJG

bisects FGH, m FGJ (7x 9)°, and m HGJ (2x 36)°. What is m FGH?

F 54° H 108°

G 86°

11. An angle measuring 22° is bisected. What is the measure of each of the two new angles?

A 11° C 33°

B 22°

12. Which angle forms a linear pair with MPS? (Hint: Makes a line with)

F RPN H MPJ

G RPM

13. If m Q (8x 40)°, what is the measure of its supplement?

A (130 8x)° C 90°

B (220 8x)°

15

Chapter

x

15

Chapter

1

CS10_G_MEIW710822_C01QZa-a.indd 15 4/2/11 4:00:38 AM



USING FORMULAS IN GEOMETRY

Practice A 2. P 2A 2w 3. area

4. 12

A bh 5. 30 yd

6. 54 yd2 7. 24 cm 8. 24 cm2 9. diameter 10. center 11. A r2

12. around 13. C 2 r or C d 14.

Problem Solving 2. 100; 60; 100; 60; 6,000 3. A 4. G

MIDPOINT AND DISTANCE IN THE COORDINATE PLANE

Practice A

2. coordinates 3. 11 , 02

§ ·¨ ¸© ¹

4. (0, 1) 5. 11 , 12

§ ·¨ ¸© ¹

6. ( 1, 3) 7. 3 miles 8. 4 miles

Problem Solving

2. 36; 78; 1,296; 6,084; 7,380; 7,380 ; 85.9

3. B 4. H

TRANSFORMATIONS IN THE COORDINATE PLANE

Practice A 2. a 3. d

4. c 5. b 6. 2; ABCD A B C D 7. 1; UHIJ UH I J 8. reflection;

Problem Solving 2. 5 3; 8; 0.5 3; 2.5; 8, 2.5 3. C 4. H

Foundations for Geometry Section A Quiz 1. A 8. G 2. F 9. A 3. B 10. F 4. H 11. A 5. B 12. G 6. H 13. B 7. C

Foundations for Geometry Section B Quiz 1. C 5. A 2. G 6. G 3. B 7. A 4. F 8. F

Foundations for Geometry Chapter Test 1. C 11. C 2. B 12. A 3. C 13. A 4. B 14. C 5. B 15. B 6. B 16. B 7. A 17. A 8. C 18. A 9. A 19. A 10. A 20. A

212

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CS10_G_MEIW710822_C01AK.indd 212 402011 4:20:26 AM



USING FORMULAS IN GEOMETRY

Practice A 2. P 2A 2w 3. area

4. 12

A bh 5. 30 yd

6. 54 yd2 7. 24 cm 8. 24 cm2 9. diameter 10. center 11. A r2

12. around 13. C 2 r or C d 14.

Problem Solving 2. 100; 60; 100; 60; 6,000 3. A 4. G

MIDPOINT AND DISTANCE IN THE COORDINATE PLANE

Practice A

2. coordinates 3. 11 , 02

§ ·¨ ¸© ¹

4. (0, 1) 5. 11 , 12

§ ·¨ ¸© ¹

6. ( 1, 3) 7. 3 miles 8. 4 miles

Problem Solving

2. 36; 78; 1,296; 6,084; 7,380; 7,380 ; 85.9

3. B 4. H

TRANSFORMATIONS IN THE COORDINATE PLANE

Practice A 2. a 3. d

4. c 5. b 6. 2; ABCD A B C D 7. 1; UHIJ UH I J 8. reflection;

Problem Solving 2. 5 3; 8; 0.5 3; 2.5; 8, 2.5 3. C 4. H

Foundations for Geometry Section A Quiz 1. A 8. G 2. F 9. A 3. B 10. F 4. H 11. A 5. B 12. G 6. H 13. B 7. C

Foundations for Geometry Section B Quiz 1. C 5. A 2. G 6. G 3. B 7. A 4. F 8. F

Foundations for Geometry Chapter Test 1. C 11. C 2. B 12. A 3. C 13. A 4. B 14. C 5. B 15. B 6. B 16. B 7. A 17. A 8. C 18. A 9. A 19. A 10. A 20. A

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CS10_G_MEIW710822_C01AK.indd 212 402011 4:20:26 AM



Answers for the chapter Foundations for Geometry

UNDERSTANDING POINTS, LINES, AND PLANES

Practice A 1. point A and point C

2. point B

3. point A, point B, and point C

4. line 5. line

6. plane 7. plane

8. point T and point U

9. one 10. point U

11.

12. PQ

HJJG

Practice B 1. Possible answers: plane BCD; plane BED

2. , , ,orBD BC BE CE

3. Possible answers: ; ;EC BC BEHJJG HJJG HJJG

4. Points B, C, and E 5. Possible answers: points B, C, and D or

point B, E, and D 6. point B

7. BCJJJG

and BEJJJG

8. points X, Y, and Z 9. point Z

10. XZHJJG

and YZHJJG

11. XYHJJJG

12.

13.

14.

Practice C 1. A plane is named with three noncollinear

points. H, I, and J are collinear. 2. Possible answers: plane HIK; plane HJK;

plane IJK

3. , , , , , andHI HJ IJ IH JH JIHJG HJJG HJG HJG HJJG HJG

4. STJJJG

and TSJJJG

are not the same figure because ST

JJJG has its endpoint at S and

TSJJJG

has its endpoint at T.

5. STJJJG

and TSJJJG

are not opposite rays because they do not have the same endpoint.

6. a line 7. point, line, plane 8. Through any three noncollinear points

there is exactly one plane containing them. 9. If two planes intersect, then they intersect

in exactly one line.

10.

Reteach 1. �•W

2.

3. 4.

5. line CD or CDHJJG

6. ray ST or STJJJG

7. plane LMN; plane Q 8. segment WX; WX

9. Possible answers: A, P, and B; C, P, and D; J, D, and K

10. Sample answer: A, P, and D 11. Sample answer: C, P, B, and D 12. Sample answer: J, D, P, and B

13. ABHJJG

and JKHJJG

14. point D

A1

x-1

A1

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CS10_G_MECR710617_C01_AK.indd 1 4/14/11 3:02:22 PM

Name ________________________________________ Date ___________________ Class __________________



Geometric Reasoning Chapter Test Form A

Circle the best answer. 1. What group of items is next in the pattern?

A

B

2. Which conjecture is true?

A An even number plus 3 is always even.

B An even number plus 3 is always prime.

C An even number plus 3 is always odd.

D A prime number plus 3 is always even.

3. Given: Jennifer sings alto in the school

choir. The choir has four voice parts. The

female voice parts are soprano and alto.

The male voice parts are tenor and bass.

What conclusion can be drawn?

A Jennifer sings a female voice part in

the choir.

B There are no basses in the choir.

4. Which conditional statement is true?

A If two angles are acute, then they are

complementary.

B If an angle is acute, then its measure

is less than 90 .

5. What is the converse of “If there are

clouds in the sky, then it is raining”?

A If it is raining, then there are clouds in

the sky.

B If it is not raining, then there are

clouds in the sky.

C If it is raining, then there are no

clouds in the sky.

D If it is not raining, then there are no

clouds in the sky.

6. Given: Pluto is the only planet other than

Earth with only one moon. A student is

looking through a telescope at a planet

that has only one moon. What conclusion

can be drawn?

A The student is not looking at Pluto.

B The student is looking at Pluto.

7. Given: If two angles are complementary,

then both angles measure less than 90 .

Angles that measure less than 90 are

acute. 1 and 2 are complementary.


A Only 1 is acute.

B Only 2 is acute.

C Both angles are acute.

D Neither angle is acute.

8. Which completes the statement to form a

true biconditional?

x2 1 if and only if ________.

A x 1

B |x| 1

9. Which property is used in solving

y 3 11?

A Symm. Prop. of

B Div. Prop. of

C Mult. Prop. of

D Subtr. Prop. of

10. Which is an example of the Reflexive

Property of Congruence?

A AB EF

B EF EF

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CS10_G_MEAR710334_C02MCCT.indd 27 405011 12:00:45 PM



Answer Key Geometric Reasoning


1. D 5. B

2. H 6. F

3. C 7. D

4. F


1. B 4. J 7. B

2. J 5. A 8. H

3. C 6. H 9. C


1. B 6. B 11. C

2. C 7. C 12. B

3. A 8. B 13. A

4. B 9. D 14. A

5. A 10. B


1. A 8. H

2. H 9. A

3. C 10. J

4. H 11. C

5. B 12. H

6. J 13. C

7. A 14. F


1. C 8. G

2. H 9. D

3. A 10. G

4. J 11. D

5. C 12. H

6. H 13. D

7. B 14. G


1. 17 2. Possible answer: receive 3. Hypothesis: It is raining.

Conclusion: There are clouds in the sky. 4. True 5. If two angles have the same measure,

then they are congruent. 6. valid 7. valid 8. A rectangle is a square if and only if it

has four congruent sides. 9. x 5 12 Given equation

x 5 5 12 5 Subtr. Prop. of x 7 Simplify.

10. A 11. theorem 12. Def. of s 13. m A m B 180 14. False

Chapter Test Form B: Free Response

1. 21 2. Possible answer: 9 3 6 3. Hypothesis: An angle has a measure

less than 90 . Conclusion: The angle is acute.

4. False 5. If the sum of two whole numbers is not

even, then both addends are not even. 6. valid 7. not valid 8. A rectangle is a square if and only if it has

four congruent sides. 9. 5m 3 22 Given equation

5m 3 3 22 3 Add. Prop. of 5m 25 Simplify.

5 255 5m Div. Prop. of

m 5 Simplify.

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CS10_G_MEAR710334_C02AK.indd 245 4/12/11 11:19:00 PM





1. D 5. B

2. H 6. F

3. C 7. D

4. F


1. B 4. J 7. B

2. J 5. A 8. H

3. C 6. H 9. C


1. B 6. B 11. C

2. C 7. C 12. B

3. A 8. B 13. A

4. B 9. D 14. A

5. A 10. B


1. A 8. H

2. H 9. A

3. C 10. J

4. H 11. C

5. B 12. H

6. J 13. C

7. A 14. F


1. C 8. G

2. H 9. D

3. A 10. G

4. J 11. D

5. C 12. H

6. H 13. D

7. B 14. G
















m 5 Simplify.

245245


Name ________________________________________ Date ___________________ Class __________________



Geometric Reasoning Chapter Test Form B

Circle the best answer. 1. What is the next item in the pattern?

1, 2, 4, 8, . . .

A 16 C 4

B 4 D 16

2. Which is a counterexample that shows

that the following conjecture is false: “If

1 and 2 are supplementary, then one

of the angles is obtuse”?

F m 1 45 and m 2 45

G m 1 53 and m 2 127

H m 1 90 and m 2 90

J m 1 100 and m 2 80

3. Given: All snarfs are yelbs. All yelbs are

blue. Migs can be either green or pink.

Some slokes are snarfs. What conclusion

can be drawn?

A Some migs are snarfs.

B Some snarfs are green.

C Some slokes are yelbs.

D All slokes are migs.

4. Given the conditional statement “If it is

January, then it is winter in the United

States,” which is true?

F the converse of the conditional

G the inverse of the conditional

H the contrapositive of the conditional

J Not here

5. What is the inverse of the conditional

statement “If a number is divisible by 6,

then it is divisible by 3”?

A If a number is divisible by 3, then it is

divisible by 6.

B If a number is not divisible by 6, then

it is not divisible by 3.

C If a number is not divisible by 3, then

it is not divisible by 6.

D If a number is not divisible by 6, then

it is divisible by 3.

6. Given: If one angle of a triangle is a right

angle, then the other two angles are both

acute. A triangle has a 45 angle.


F One of the other two angles is 90 .

G One of the other two angles is obtuse.

H All three angles are acute.

J No conclusion can be drawn.

7. Which symbolic statement represents the

Law of Syllogism?

A If p q and q r are true statements,

then p r is a true statement.

B If p q and p r are true statements,

then q r is a true statement.

C If p q and r q are true statements,

then q p is a true statement.

D If p r and q r are true statements,

then p q is a true statement.

8. Which is a biconditional statement of the

conditional statement “If x3 1, then

x 1”?

F If x 1, then x3 1.

G x3 1 if x 1.

H x3 1 if and only if x 1.

J x 1 x3 1.

9. Which property is NOT used when

solving 15 2x 1?

A Reflex. Prop. of

B Add. Prop. of

C Div. Prop. of

D Sym. Prop. of

10. Identify the property that justifies the

statement “If B A, then

A B.”

F Sym. Prop. of

G Reflex. Prop. of

H Trans. Prop. of

J Sym. Prop. of

Name ________________________________________ Date ___________________ Class __________________



Geometric Reasoning Chapter Test Form A continued

11. Which item can be given as a statement in a proof?

A Given

B Def. of comp.

C m 1 m 2 180

D Trans. Prop. of

12. Given the partially completed two-column proof, which is the reason for Step 3?

Statements Reasons

1. AE FB 1. Given

2. FB EF 2. Given

3. AE EF 3. ?

A Def. of midpoint

B Trans. Prop. of

13. Given the two-column proof, how many boxes will be needed for the flowchart proof?

Statements Reasons

1. 1 and 2 are rt. .

1. Given

2. m 1 90 , m 2 90

2. Def. of rt.

3. m 1 m 2 3. Trans. Prop. of

4. 1 2 4. Def. of

A 4

B 8

14. A sentence in a paragraph proof states “m A m B 180 by the definition of supplementary angles.” In a flowchart proof, which box represents this sentence? A

B

Chapter

x

29

Chapter

2

29

CS10_G_MEAR710334_C02MCCT.indd 29 405011 12:00:46 PM





1. D 5. B

2. H 6. F

3. C 7. D

4. F


1. B 4. J 7. B

2. J 5. A 8. H

3. C 6. H 9. C


1. B 6. B 11. C

2. C 7. C 12. B

3. A 8. B 13. A

4. B 9. D 14. A

5. A 10. B


1. A 8. H

2. H 9. A

3. C 10. J

4. H 11. C

5. B 12. H

6. J 13. C

7. A 14. F


1. C 8. G

2. H 9. D

3. A 10. G

4. J 11. D

5. C 12. H

6. H 13. D

7. B 14. G
















m 5 Simplify.

245245






1. D 5. B

2. H 6. F

3. C 7. D

4. F


1. B 4. J 7. B

2. J 5. A 8. H

3. C 6. H 9. C


1. B 6. B 11. C

2. C 7. C 12. B

3. A 8. B 13. A

4. B 9. D 14. A

5. A 10. B


1. A 8. H

2. H 9. A

3. C 10. J

4. H 11. C

5. B 12. H

6. J 13. C

7. A 14. F


1. C 8. G

2. H 9. D

3. A 10. G

4. J 11. D

5. C 12. H

6. H 13. D

7. B 14. G
















m 5 Simplify.

245245






1. D 5. B

2. H 6. F

3. C 7. D

4. F


1. B 4. J 7. B

2. J 5. A 8. H

3. C 6. H 9. C


1. B 6. B 11. C

2. C 7. C 12. B

3. A 8. B 13. A

4. B 9. D 14. A

5. A 10. B


1. A 8. H

2. H 9. A

3. C 10. J

4. H 11. C

5. B 12. H

6. J 13. C

7. A 14. F


1. C 8. G

2. H 9. D

3. A 10. G

4. J 11. D

5. C 12. H

6. H 13. D

7. B 14. G
















m 5 Simplify.

245245




Contrapositive: If A is not obtuse, then m A 140°; true

USING DEDUCTIVE REASONING TO VERIFY CONJECTURES

Practice A 1. Deductive 2. q 3. deductive reasoning 4. inductive reasoning 5. A person sees penguins. The person is in Antarctica. valid 6. A person sees a polar bear. The person is in the Arctic. not valid 7. Syllogism 8. your feet hurt

Practice B 1. inductive reasoning 2. deductive reasoning 3. invalid 4. invalid 5. valid 6. valid 7. invalid 8. valid

9. EF and MN could be perpendicular. 10. Becky’s blood pressure is relatively low.

Practice C

1. 2.

3. 4. 5. Possible answer: The Law of Detachment

states that if p q is true and p is true, then q is true. Also by the Law of Detachment, if q r is true and q is true, then r is true. So when p is true, r is true, and thus p r is true.

6. If p q and q r and r s are true statements, then p s is a true statement.

7. A sequel will be made.

Reteach 1. deductive 2. inductive 3. deductive 4. valid 5. invalid 6. valid 7. valid 8. invalid 9. ULMN and UL M N have equal

perimeters. 10. R and S are supplementary to the

same angle.

Challenge 1. Possible answer: If Anna rides the bus

with the person from New Jersey, then Anna is not from New Jersey. So Anna must be from California or Texas.

2. a. Yes; the conditional is true and the hypothesis is true.

b. No; a true conditional and a true conclusion do not necessarily make the hypothesis true. Jake could be from a different West Coast state.

3. Possible answer: If Jake likes to go to his friend’s swim meets, then he is not on the swim team. Conjecture: Jake is not on the swim team. So Jake is on Student Council or in the math club.

4. Jake is from Texas and is on Student Council. Anna is from California and is in the math club. Ling is from New Jersey and is on the swim team.

Problem Solving 1. Conclusion: Mt. Kilauea’s eruption in

Hawaii was a category 1 eruption. 2. No valid conclusion can be made.

Possible answer: The negation of the hypothesis does not produce a valid conclusion given a true conditional.

3. Conclusion: The eruption of the volcano in Stromboli, Italy, produced a plume of ash 1–5 kilometers high.

4. B 5. J



Reading Strategies 1. Conjecture: m BAC m CAD Hypothesis: Two angles are congruent. valid, Detachment 2. Conjecture: If 90° m S 180°, then it

is not a right angle. p: The measure of S is greater than 90°

and less than 180°. q: The angle is obtuse. r: The angle is not a right angle. valid, Syllogism

BICONDITIONAL STATEMENTS AND DEFINITIONS

Practice A 1. converse 2. q; p 3. If a cat is purring, then it is happy. 4. If a figure is straight and has two

endpoints, then it is a segment. 5. Two angles share a side if and only if

they are adjacent. 6. Your temperature is normal if and only if it

is 98.6°F. 7. True; False; False; Sample answer: x 4 8. True; False; False; Sample answer: It is

midnight. 9. True

Practice B 1. Conditional: If the tea kettle is whistling,

then the water is boiling. Converse: If the water is boiling, then the

tea kettle is whistling. 2. Conditional: If a biconditional is true, then

the conditional and converse are both true.

Converse: If the conditional and converse are both true, then the biconditional is true.

3. Converse: If n 1 is divisible by 2, then n is an odd number.

Biconditional: n is an odd number if and only if n 1 is divisible by 2.

4. Converse: If an angle measures between 90° and 180°, then the angle is obtuse.

Biconditional: An angle is obtuse if and only if it measures between 90° and 180°.

5. No; sample answer: The switch could be off.

6. No; possible answer: Leap years have a Feb. 29th.

7. A figure is a cube if and only if it is a three-dimensional solid with six square faces.

8. A person is a doofus if and only if the person is Tanya’s younger brother.

Practice C 1. yes 2. No; the abnormal XXY male also has

exactly one Y chromosome. 3. No; the abnormal XXY male also has a

pair of X chromosomes. 4. yes 5. Possible answer: Postulates are

statements that are accepted as true without proof. Definitions are statements that describe mathematical objects and provide vocabulary for investigating these objects.

6. postulate 7. definition 8. postulate 9. postulate 10. definition

Reteach 1. Conditional: If Lindsay takes photos for the

yearbook, then she doesn’t play soccer. Converse: If Lindsay doesn’t play soccer, then she will take photos for the yearbook.

2. Conditional: If m ABC m CBD, then BCJJJG

is an angle bisector of ABD. Converse: If BC

JJJG is an angle bisector of

ABD, then m ABC m CBD. 3. Converse: If each song costs $0.99, then

you can download 6 songs for $5.94. Biconditional: You can download 6 songs

for $5.94 if and only if each song costs $0.99.

A12

x-3

A12

2-3




Contrapositive: If A is not obtuse, then m A 140°; true

USING DEDUCTIVE REASONING TO VERIFY CONJECTURES

Practice A 1. Deductive 2. q 3. deductive reasoning 4. inductive reasoning 5. A person sees penguins. The person is in Antarctica. valid 6. A person sees a polar bear. The person is in the Arctic. not valid 7. Syllogism 8. your feet hurt

Practice B 1. inductive reasoning 2. deductive reasoning 3. invalid 4. invalid 5. valid 6. valid 7. invalid 8. valid

9. EF and MN could be perpendicular. 10. Becky’s blood pressure is relatively low.

Practice C

1. 2.

3. 4. 5. Possible answer: The Law of Detachment

states that if p q is true and p is true, then q is true. Also by the Law of Detachment, if q r is true and q is true, then r is true. So when p is true, r is true, and thus p r is true.

6. If p q and q r and r s are true statements, then p s is a true statement.

7. A sequel will be made.

Reteach 1. deductive 2. inductive 3. deductive 4. valid 5. invalid 6. valid 7. valid 8. invalid 9. ULMN and UL M N have equal

perimeters. 10. R and S are supplementary to the

same angle.

Challenge 1. Possible answer: If Anna rides the bus

with the person from New Jersey, then Anna is not from New Jersey. So Anna must be from California or Texas.

2. a. Yes; the conditional is true and the hypothesis is true.

b. No; a true conditional and a true conclusion do not necessarily make the hypothesis true. Jake could be from a different West Coast state.

3. Possible answer: If Jake likes to go to his friend’s swim meets, then he is not on the swim team. Conjecture: Jake is not on the swim team. So Jake is on Student Council or in the math club.

4. Jake is from Texas and is on Student Council. Anna is from California and is in the math club. Ling is from New Jersey and is on the swim team.

Problem Solving 1. Conclusion: Mt. Kilauea’s eruption in

Hawaii was a category 1 eruption. 2. No valid conclusion can be made.

Possible answer: The negation of the hypothesis does not produce a valid conclusion given a true conditional.

3. Conclusion: The eruption of the volcano in Stromboli, Italy, produced a plume of ash 1–5 kilometers high.

4. B 5. J



Reading Strategies 1. Conjecture: m BAC m CAD Hypothesis: Two angles are congruent. valid, Detachment 2. Conjecture: If 90° m S 180°, then it

is not a right angle. p: The measure of S is greater than 90°

and less than 180°. q: The angle is obtuse. r: The angle is not a right angle. valid, Syllogism

BICONDITIONAL STATEMENTS AND DEFINITIONS

Practice A 1. converse 2. q; p 3. If a cat is purring, then it is happy. 4. If a figure is straight and has two

endpoints, then it is a segment. 5. Two angles share a side if and only if

they are adjacent. 6. Your temperature is normal if and only if it

is 98.6°F. 7. True; False; False; Sample answer: x 4 8. True; False; False; Sample answer: It is

midnight. 9. True

Practice B 1. Conditional: If the tea kettle is whistling,

then the water is boiling. Converse: If the water is boiling, then the

tea kettle is whistling. 2. Conditional: If a biconditional is true, then

the conditional and converse are both true.

Converse: If the conditional and converse are both true, then the biconditional is true.

3. Converse: If n 1 is divisible by 2, then n is an odd number.

Biconditional: n is an odd number if and only if n 1 is divisible by 2.

4. Converse: If an angle measures between 90° and 180°, then the angle is obtuse.

Biconditional: An angle is obtuse if and only if it measures between 90° and 180°.

5. No; sample answer: The switch could be off.

6. No; possible answer: Leap years have a Feb. 29th.

7. A figure is a cube if and only if it is a three-dimensional solid with six square faces.

8. A person is a doofus if and only if the person is Tanya’s younger brother.

Practice C 1. yes 2. No; the abnormal XXY male also has

exactly one Y chromosome. 3. No; the abnormal XXY male also has a

pair of X chromosomes. 4. yes 5. Possible answer: Postulates are

statements that are accepted as true without proof. Definitions are statements that describe mathematical objects and provide vocabulary for investigating these objects.

6. postulate 7. definition 8. postulate 9. postulate 10. definition

Reteach 1. Conditional: If Lindsay takes photos for the

yearbook, then she doesn’t play soccer. Converse: If Lindsay doesn’t play soccer, then she will take photos for the yearbook.

2. Conditional: If m ABC m CBD, then BCJJJG

is an angle bisector of ABD. Converse: If BC

JJJG is an angle bisector of

ABD, then m ABC m CBD. 3. Converse: If each song costs $0.99, then

you can download 6 songs for $5.94. Biconditional: You can download 6 songs

for $5.94 if and only if each song costs $0.99.

A12

x-3

A12

2-3


2.5*PRACTICE*B*20.*and*21.*

%22.*

%23.*

%%%%%%



4. Converse: If a figure is a decagon, then it has 10 sides.

Biconditional: A figure has 10 sides if and only if it is a decagon.

5. False; possible answer: members of flag corps perform during halftime.

6. true 7. False; possible answer: a 2 and b 6 8. A triangle is isosceles if and only if it has

at least two congruent sides. 9. You use deductive reasoning if and only if

you use facts, definitions, and properties to draw conclusions.

Challenge 1. Hypoth-

esis Conclu-

sion Condi-tional

Con-verse

Bicondi-tional

p q p q q p p q T T T T T T F F T F F T T F F F F T T T

2. when p and q are both true or when p and q are both false

3. The truth values are the same except when the hypothesis is false and the conclusion is true. In this case, the conditional is true and the biconditional is false.

4. p q; both are true except for the case when p is true and q is false.

5. Possible answer: If an angle measures 105°, then it is obtuse. Biconditional: An angle measures 105° if and only if it is obtuse. The biconditional is false because the converse is false.

6. M is the midpoint of AB if and only if M is on AB and AM MB.

7. A figure is a bisector of a segment if and only if it is a line, ray, or segment that intersects the segment at its midpoint.

8. A segment is a chord of a circle if and only if the endpoints of the segment are on the circle.

Problem Solving 1. No; marathon races are also mass-

started, so the conditional is false. 2. No; time is also a factor in freeride races,

so the converse is false. 3. Yes; a mountain bike race covers 250

kilometers if and only if it is a marathon race.

4. No; a downhill race does not contain cliffs, drops, and ramps, so the converse is false.

5. C 6. G

Reading Strategies 1. Biconditional statement: Possible answer:

m WXY �m YXZ if and only if XYJJJJG

is the angle bisector.

Conditional: Answers will vary. Sample answer: If m WXY m YXZ, then XY

JJJJG

is the angle bisector. Converse: Possible answer: If XY

JJJJG is the

angle bisector, then m WXY m YXZ. Definition of an angle bisector: Possible

answer: An angle bisector divides an angle into two angles of equal measure.

2. Biconditional statement: Possible answer: FGH and QRS are complementary

angles if and only if m FGH m QRS 90°.

Conditional: Possible answer: If FGH and QRS are complementary angles, then m FGH m QRS 90°.

Converse: Possible answer: If m FGH m QRS 90°, then they are complementary angles.

Definition of complementary angles: Possible answer: Two angles whose measures sum to 90° are complementary angles.

ALGEBRAIC PROOF

Practice A 1. F 2. C 3. J 4. E 5. A 6. I



7. G 8. K

9. L 10. D

11. H 12. B

13. 8; 20.32; c; 20.32

14. Seg. Add. Post.; Subst.; Simplify.; Subtr.

Prop. of ; Mult. Prop. of

Practice B 1.

1

5 10 5 35

aª º« »¬ ¼

(Mult. Prop. of )

a 10 15 (Simplify.)

a 10 10 15 10 (Subtr. Prop. of )

a –25 (Simplify.)

2.

t 6.5 t 3t 1.3 t (Subtr. Prop. of )

6.5 2t 1.3 (Simplify.)

6.5 1.3 2t 1.3 + 1.3 (Add. Prop. of )

7.8 2t (Simplify.)

7.8 2

2 2

t (Div. Prop. of )

3.9 t (Simplify.)

t 3.9 (Symmetric Prop. of

)

3.

P 2(A w) (Given)

91

2

12 1

4

§ ·¨ ¸© ¹A (Subst. Prop. of )

91

2 2A 2

1

2 (Distrib. Prop.)

91

2 2

1

2 2A 2

1

2 2

1

2 (Subtr. Prop.

of )

7 2A (Simplify.)

7 2

2

A (Div. Prop. of

)

31

2 A (Simplify.)

A 31

2 (Symmetric

Prop. of )

4.

Seg. Add. Post.

Subst. Prop. of

Simplify.

Add. Prop. of

Subtr. Prop. of

Div. Prop. of

5. Symmetric Prop. of

6. Reflexive Prop. of


8. Transitive Prop. of or Subst.

Practice C 1.

m 1 m 2 90° (Given)

m 2 m 3 180° (Given)

m 2 m 3 (m 1 m 2)

180° 90° (Subtr. Prop. of )

m 3 m 1 90° (Simplify.)

m 3 m 1 90° (Add. Prop. of )

2.

XYZ ABC (Given)

ZYX XYZ (Reflexive Prop. of ) ZYX ABC (Trans. Prop. of )

m ZYX m ABC (Def. of ) ABD CBD (Def. of bisector)

m ABD m CBD (Def. of ) m ABC m ABD

m CBD ( Add. Post.)

m ABC m CBD m CBD (Subst. Prop. of )

m ABC 2m CBD (Simplify.)

m ZYX 2m CBD (Subst. Prop. of ) 3. (x y) a; a(c d) ac ad; ac ad

c(x y) d(x y); c(x y) d(x y) cx

cy dx dy; (x y)(c d) cx cy

dx dy 4. Possible answer: The Substitution

Property states that if a b, then b can

be substituted for a in any expression.

Applying the Symmetric Property to the

Substitution Property shows that if b a,

then a can be substituted for b in any

A15A15











esis Conclu-

sion Condi-tional

Con-verse

Bicondi-tional














5. C 6. G





JJJJG


JJJJG is the








ALGEBRAIC PROOF




7. G 8. K

9. L 10. D

11. H 12. B

13. 8; 20.32; c; 20.32



Practice B 1.

1

5 10 5 35

aª º« »¬ ¼

(Mult. Prop. of )

a 10 15 (Simplify.)

a 10 10 15 10 (Subtr. Prop. of )

a –25 (Simplify.)

2.



6.5 1.3 2t 1.3 + 1.3 (Add. Prop. of )

7.8 2t (Simplify.)

7.8 2

2 2

t (Div. Prop. of )

3.9 t (Simplify.)


)

3.

P 2(A w) (Given)

91

2

12 1

4


91

2 2A 2

1

2 (Distrib. Prop.)

91

2 2

1

2 2A 2

1

2 2

1

2 (Subtr. Prop.

of )

7 2A (Simplify.)

7 2

2

A (Div. Prop. of

)

31

2 A (Simplify.)

A 31

2 (Symmetric

Prop. of )

4.

Seg. Add. Post.

Subst. Prop. of

Simplify.

Add. Prop. of

Subtr. Prop. of

Div. Prop. of





Practice C 1.

m 1 m 2 90° (Given)

m 2 m 3 180° (Given)

m 2 m 3 (m 1 m 2)



m 3 m 1 90° (Add. Prop. of )

2.

XYZ ABC (Given)




m CBD ( Add. Post.)












A15A15











esis Conclu-

sion Condi-tional

Con-verse

Bicondi-tional














5. C 6. G





JJJJG


JJJJG is the








ALGEBRAIC PROOF




7. G 8. K

9. L 10. D

11. H 12. B

13. 8; 20.32; c; 20.32



Practice B 1.

1

5 10 5 35

aª º« »¬ ¼

(Mult. Prop. of )

a 10 15 (Simplify.)

a 10 10 15 10 (Subtr. Prop. of )

a –25 (Simplify.)

2.



6.5 1.3 2t 1.3 + 1.3 (Add. Prop. of )

7.8 2t (Simplify.)

7.8 2

2 2

t (Div. Prop. of )

3.9 t (Simplify.)


)

3.

P 2(A w) (Given)

91

2

12 1

4


91

2 2A 2

1

2 (Distrib. Prop.)

91

2 2

1

2 2A 2

1

2 2

1

2 (Subtr. Prop.

of )

7 2A (Simplify.)

7 2

2

A (Div. Prop. of

)

31

2 A (Simplify.)

A 31

2 (Symmetric

Prop. of )

4.

Seg. Add. Post.

Subst. Prop. of

Simplify.

Add. Prop. of

Subtr. Prop. of

Div. Prop. of





Practice C 1.

m 1 m 2 90° (Given)

m 2 m 3 180° (Given)

m 2 m 3 (m 1 m 2)



m 3 m 1 90° (Add. Prop. of )

2.

XYZ ABC (Given)




m CBD ( Add. Post.)












A15A15


24:27.*

%%Minutes:Degrees:Seconds*28*** a.* 40˚2’30’’*29* b.* 35˚47’46’’**Clock*problems:*30.* 3:50.**:*155˚;***31.* 1:35:* 167.5˚**32.* 8:15* 157.5˚**Proofs*See*next*pages*for*handwritten;*all*work**33.*

%34.%

*35.*

**Drawing*conclusions:*36.%%%% XW %≅ % XV %37.%%∠PAR,%∠ART%are%right%angles%38.%%BF %≅ %FD %%39.%%∠AEL%was%trisected%40.%∠PQS%is%a%right%angle%;%RS ⊥ %PQ %










esis Conclu-

sion Condi-tional

Con-verse

Bicondi-tional














5. C 6. G





JJJJG


JJJJG is the








ALGEBRAIC PROOF




7. G 8. K

9. L 10. D

11. H 12. B

13. 8; 20.32; c; 20.32



Practice B 1.

1

5 10 5 35

aª º« »¬ ¼

(Mult. Prop. of )

a 10 15 (Simplify.)

a 10 10 15 10 (Subtr. Prop. of )

a –25 (Simplify.)

2.



6.5 1.3 2t 1.3 + 1.3 (Add. Prop. of )

7.8 2t (Simplify.)

7.8 2

2 2

t (Div. Prop. of )

3.9 t (Simplify.)


)

3.

P 2(A w) (Given)

91

2

12 1

4


91

2 2A 2

1

2 (Distrib. Prop.)

91

2 2

1

2 2A 2

1

2 2

1

2 (Subtr. Prop.

of )

7 2A (Simplify.)

7 2

2

A (Div. Prop. of

)

31

2 A (Simplify.)

A 31

2 (Symmetric

Prop. of )

4.

Seg. Add. Post.

Subst. Prop. of

Simplify.

Add. Prop. of

Subtr. Prop. of

Div. Prop. of





Practice C 1.

m 1 m 2 90° (Given)

m 2 m 3 180° (Given)

m 2 m 3 (m 1 m 2)



m 3 m 1 90° (Add. Prop. of )

2.

XYZ ABC (Given)




m CBD ( Add. Post.)












A15A15


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