Chapter Foundations for Geometry - Mr. Caronna's ...caronnaclassroom.weebly.com/uploads/1/3/3/8/13388109/gh...Which names a pair of opposite rays? A AB JJJG and BG JJJG C AB JJJG and

Test 2: additional practice problems 1.1-‐1.4, 1.6, 2.2, 2.3(syllogism), 2.5

CHAPTER 2

Name ________________________________________ Date ___________________ Class __________________

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

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Foundations for Geometry Chapter Test Form A




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


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

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Chapter

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7


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Foundations for Geometry Chapter Test Form B




A plane AE C plane BAD

B plane A D plane BAC


F AD H AC

G BC J BE

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

A DAJJJG

C CAJJJG

B BCJJJG

D ABJJJG

4. Name the intersection of plane P and line m.

F line n H AC

G point A J AE

5. What is the measure of RT ?

A 5 C 26

B 16 D 40

6. Given LM MP and L, M, and P are collinear, which of the following BEST describes the relationship of L, M, and P ?

F LM MP

G M is the midpoint of .LP

H M bisects .LP

J All of the above

Use the figure for Exercises 7 and 8.

7. Which term describes PMQ?

A obtuse C right

B straight D acute

8. What is m PMN?

F 22 H 68

G 90 J 112

9. Which angles are adjacent and form a linear pair?

A 1 and 2 C 2 and 3

B 3 and 4 D 1 and 5

10. If m A (4x 2) , what is the measure of the complement of A?

F 90 H (178 4x)

G (4x 92) J (88 4x)

Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form A continued

11. If m B x , what is the measure of a supplement of B? A 90 C (90 x) B 180 D (180 x)

12. What is the perimeter of a square with s 8 centimeters? A 32 cm B 64 cm

13. What is the area of a triangle with a base of 6 inches and a height of 3 inches? A 9 in2 B 18 in2

14. What is the approximate area of a circle with a radius of 4 feet? Use 3.14 for . A 12.56 ft2 C 50.24 ft2 B 25.12 ft2 D 200.96 ft2

15. What are the coordinates of the midpoint of GH with endpoints G( 2, 5) and H(4, 1)? A ( 6, 4) C ( 3, 2) B (1, 3) D (2, 6)

16. M is the midpoint of RS and R has coordinates (2, 5). M has coordinates (6, 9). Find the coordinates of S. A (4.5, 6.5) C (4, 4) B (10, 13) D (16, 16)

17. Use the Distance Formula to find VW.

A 5 C 9

B 29 D 25

18. Use the Pythagorean Theorem to find the length of the hypotenuse.

A 10 C 48 B 14 D 100

19. What transformation is shown?

A translation B reflection

20. What rule would you use to translate a figure in the coordinate plane 2 units to the right? A (x, y) (x 2, y) B (x, y) (x, y 2)

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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


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


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

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Name ________________________________________ Date ___________________ Class __________________







point D?




F BE H BC

G GB J AC


A ABJJJG

and BGJJJG

C ABJJJG

and BAJJJG

B BCJJJG

and ABJJJG

D BDJJJG

and BEJJJG


F line n H line m

G point B J AC


A 2 C 5

B 3 D 6


F LM MP


H M bisects .LP


7. Find m LMQ.

A 68 C 112

B 90 D 158

8. XZJJJG


F 45 H 135

G 90 J 180


A 1 and 5 C 2 and 4

B 2 and 3 D 4 and 5

Name ________________________________________ Date ___________________ Class __________________













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




Chapter

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10

Chapter

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10


Name ________________________________________ Date ___________________ Class __________________







point D?




F BE H BC

G GB J AC


A ABJJJG

and BGJJJG

C ABJJJG

and BAJJJG

B BCJJJG

and ABJJJG

D BDJJJG

and BEJJJG


F line n H line m

G point B J AC


A 2 C 5

B 3 D 6


F LM MP


H M bisects .LP


7. Find m LMQ.

A 68 C 112

B 90 D 158

8. XZJJJG


F 45 H 135

G 90 J 180


A 1 and 5 C 2 and 4

B 2 and 3 D 4 and 5

Name ________________________________________ Date ___________________ Class __________________













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




Chapter

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Foundations for Geometry Chapter Test Form C continued

10. The measure of A is twice the measure of its complement. What is the measure of A? F 20 H 60 G 30 J 90

11. If m B (180 x) , what is the measure of a supplement of B?

A 180 C (180 x)

B x D (90 x)

12. What is the length of a rectangle if the perimeter is 88 inches and the length is 2 inches more than the width? F 21 in. H 25 in. G 23 in. J 42 in.

13. What is the height of a triangle with an area of 16.5 square meters if the base is 5.5 meters? A 1.5 m C 6 m2 B 3 m D 6 m

14. A circle has an area of 81 square feet. What is its radius? F 9 ft H 20.5 ft G 9 ft2 J 40.5 ft

15. Given GH with endpoints G( 7, 3) and H(7, 11), what are the coordinates of the midpoint of GH ?

A (0, 4) C ( 7, 7)

B (0, 8) D ( 14, 14)

16. M is the midpoint of .RS R has coordinates ( 2, 10), and M has coordinates (3, 5). What are the coordinates of S? F (1, 15) H (8, 0)

G (0.5, 7.5) J (5, 5)

17. What is the distance from M(9, 4) to N( 1, 2)?

A 10 C 2 26

B 10 D 12

18. Given a right triangle with the length of one leg equal to 9 centimeters and the length of the hypotenuse equal to 15 centimeters, what is the length of the other leg?

F 6 cm H 306 cm

G 12 cm J 144 cm



20. A triangle has vertices A( 3, 6), B(1, 5), and C(2, 4). After a transformation, the image of the triangle has vertices A ( 3, 6), B (1, 5), and C (2, 4). Identify the transformation. F reflection across the x-axis G reflection across the y-axis H rotation J translation

Chapter

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Name ________________________________________ Date ___________________ Class __________________







point D?




F BE H BC

G GB J AC


A ABJJJG

and BGJJJG

C ABJJJG

and BAJJJG

B BCJJJG

and ABJJJG

D BDJJJG

and BEJJJG


F line n H line m

G point B J AC


A 2 C 5

B 3 D 6


F LM MP


H M bisects .LP


7. Find m LMQ.

A 68 C 112

B 90 D 158

8. XZJJJG


F 45 H 135

G 90 J 180


A 1 and 5 C 2 and 4

B 2 and 3 D 4 and 5

Name ________________________________________ Date ___________________ Class __________________













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




Chapter

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Chapter

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11


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


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

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Name ________________________________________ Date ___________________ Class __________________







A KSJJJG

C RKHJJG

B KTJJJG


F 1 H 3

G 2



A line m C line p

B line n


F 1 H 3

G 2



A 2 C 5

B 4


F 7.5 H 7.5

G 2.5




F 7 H 56

G 48


A acute C obtuse

B right

10. GJJJJG


F 54° H 108°

G 86°


A 11° C 33°

B 22°


F RPN H MPJ

G RPM


A (130 8x)° C 90°

B (220 8x)°

15

Chapter

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15

Chapter

1


Name ________________________________________ Date ___________________ Class __________________







A KSJJJG

C RKHJJG

B KTJJJG


F 1 H 3

G 2



A line m C line p

B line n


F 1 H 3

G 2



A 2 C 5

B 4


F 7.5 H 7.5

G 2.5




F 7 H 56

G 48


A acute C obtuse

B right

10. GJJJJG


F 54° H 108°

G 86°


A 11° C 33°

B 22°


F RPN H MPJ

G RPM


A (130 8x)° C 90°

B (220 8x)°

15

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Name ________________________________________ Date __________________ Class__________________



Practice B Understanding Points, Lines, and Planes


1. Name a plane. _____________________________________

2. Name a segment. ___________________________________

3. Name a line. _______________________________________

4. Name three collinear points.

_____________________________________________________________

5. Name three noncollinear points.

_________________________________________________________________________________________

6. Name the intersection of a line and a segment not on the line. _______________________

7. Name a pair of opposite rays. _________________________________________________


8. Name the points that determine plane .R

________________________________________________________

9. Name the point at which line m intersects

plane .R _____________________________________

10. Name two lines in plane R that intersect line m.

________________________________________________________

11. Name a line in plane R that does not intersect

line m. ________________________________________

Draw your answers in the space provided.

Michelle Kwan won a bronze medal in figure skating at the 2002 Salt Lake City Winter Olympic Games. 12. Michelle skates straight ahead from point L and stops

at point M. Draw her path. 13. Michelle skates straight ahead from point L and continues

through point M. Name a figure that represents her path. Draw her path.

14. Michelle and her friend Alexei start back to back at point L and skate in opposite directions. Michelle skates through point M, and Alexei skates through point K. Draw their paths.

LESSON

x-x

1-41-4

LESSON

1-1

CS10_G_MECR710617_C01L01b.indd 4 4/8/11 8:40:52 AM

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

Name ________________________________________ Date ___________________ Class __________________





A

B












the choir.




complementary.


is less than 90 .




the sky.


clouds in the sky.


clouds in the sky.


clouds in the sky.





can be drawn?








A Only 1 is acute.

B Only 2 is acute.




true biconditional?


A x 1

B |x| 1


y 3 11?

A Symm. Prop. of

B Div. Prop. of

C Mult. Prop. of

D Subtr. Prop. of



A AB EF

B EF EF

Chapter

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Chapter

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27


Name ________________________________________ Date ___________________ Class __________________





A

B












the choir.




complementary.


is less than 90 .




the sky.


clouds in the sky.


clouds in the sky.


clouds in the sky.





can be drawn?








A Only 1 is acute.

B Only 2 is acute.




true biconditional?


A x 1

B |x| 1


y 3 11?

A Symm. Prop. of

B Div. Prop. of

C Mult. Prop. of

D Subtr. Prop. of



A AB EF

B EF EF

Chapter

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Chapter

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Nam

e________________________________________

Date

__________________ C

lass__________________

Original content C

opyright © by H

olt McD

ougal. Additions and changes to the original content are the responsibility of the instructor.

Holt M

cDougal G

eometry

Practice B

Understanding Points, Lines, and Planes


1. Nam

e a plane. _____________________________________

2. Nam

e a segment.___________________________________

3. Nam

e a line._______________________________________

4. Nam

e three collinear points.

_____________________________________________________________

5. Nam

e three noncollinear points.

_________________________________________________________________________________________

6. Nam

e the intersection of a line and a segment not on the line.

_______________________

7. Nam

e a pair of opposite rays._________________________________________________


8. Nam

e the points that determine plane

.R

________________________________________________________

9. Nam

e the point at which line m

intersects

plane .

R

_____________________________________

10. Nam

e two lines in plane R

that intersect line m.

________________________________________________________

11. Nam

e a line in plane R that does not intersect

line m. ________________________________________

Draw

your answers in the space provided.

Michelle K

wan w

on a bronze medal in figure skating at the 2002 S

alt Lake C

ity Winter O

lympic G

ames.

12. Michelle skates straight ahead from

point L and stops

at point M. D

raw her path.

13. Michelle skates straight ahead from

point L and continues

through point M. N

ame a figure that represents her path.

Draw

her path. 14. M

ichelle and her friend Alexei start back to back at point L

and skate in opposite directions. M

ichelle skates through point M

, and Alexei skates through point K. D

raw their paths.

LESSON

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1-4

LESSON

1-1

CS

10_G_M

EC

R710617_C

01L01b.indd 44/8/11 8:40:52 A

M

2.3 PRACTICE B

2.5 PRACTICE B Solve each equation. Show all your steps and write a justification for each step

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


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

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Name ________________________________________ Date ___________________ Class __________________





1, 2, 4, 8, . . .

A 16 C 4

B 4 D 16





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




can be drawn?











J Not here





divisible by 6.
















Law of Syllogism?











x 1”?


G x3 1 if x 1.


J x 1 x3 1.


solving 15 2x 1?

A Reflex. Prop. of

B Add. Prop. of

C Div. Prop. of

D Sym. Prop. of



A B.”

F Sym. Prop. of

G Reflex. Prop. of

H Trans. Prop. of

J Sym. Prop. of

Name ________________________________________ Date ___________________ Class __________________





A Given

B Def. of comp.

C m 1 m 2 180

D Trans. Prop. of


Statements Reasons

1. AE FB 1. Given

2. FB EF 2. Given

3. AE EF 3. ?

A Def. of midpoint

B Trans. Prop. of


Statements Reasons


1. Given

2. m 1 90 , m 2 90

2. Def. of rt.


4. 1 2 4. Def. of

A 4

B 8


B

Chapter

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29


Name ________________________________________ Date ___________________ Class __________________





1, 2, 4, 8, . . .

A 16 C 4

B 4 D 16





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




can be drawn?











J Not here





divisible by 6.
















Law of Syllogism?











x 1”?


G x3 1 if x 1.


J x 1 x3 1.


solving 15 2x 1?

A Reflex. Prop. of

B Add. Prop. of

C Div. Prop. of

D Sym. Prop. of



A B.”

F Sym. Prop. of

G Reflex. Prop. of

H Trans. Prop. of

J Sym. Prop. of

Name ________________________________________ Date ___________________ Class __________________





A Given

B Def. of comp.

C m 1 m 2 180

D Trans. Prop. of


Statements Reasons

1. AE FB 1. Given

2. FB EF 2. Given

3. AE EF 3. ?

A Def. of midpoint

B Trans. Prop. of


Statements Reasons


1. Given

2. m 1 90 , m 2 90

2. Def. of rt.


4. 1 2 4. Def. of

A 4

B 8


B

Chapter

x

29

Chapter

2

29


Name ________________________________________ Date ___________________ Class __________________





1, 2, 4, 8, . . .

A 16 C 4

B 4 D 16





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




can be drawn?











J Not here





divisible by 6.
















Law of Syllogism?











x 1”?


G x3 1 if x 1.


J x 1 x3 1.


solving 15 2x 1?

A Reflex. Prop. of

B Add. Prop. of

C Div. Prop. of

D Sym. Prop. of



A B.”

F Sym. Prop. of

G Reflex. Prop. of

H Trans. Prop. of

J Sym. Prop. of

Name ________________________________________ Date ___________________ Class __________________





A Given

B Def. of comp.

C m 1 m 2 180

D Trans. Prop. of


Statements Reasons

1. AE FB 1. Given

2. FB EF 2. Given

3. AE EF 3. ?

A Def. of midpoint

B Trans. Prop. of


Statements Reasons


1. Given

2. m 1 90 , m 2 90

2. Def. of rt.


4. 1 2 4. Def. of

A 4

B 8


B

Chapter

x

29

Chapter

2

29


Name ________________________________________ Date __________________ Class__________________



Practice B Using Deductive Reasoning to Verify Conjectures

Tell whether each conclusion is a result of inductive or deductive reasoning. 1. The United States Census Bureau collects data on the earnings of American citizens.

Using data for the three years from 2001 to 2003, the bureau concluded that the national average median income for a four-person family was $43,527.

_________________________________________________________________________________________

2. A speeding ticket costs $40 plus $5 per mi/h over the speed limit. Lynne mentions to Frank that she was given a ticket for $75. Frank concludes that Lynne was driving 7 mi/h over the speed limit.

_________________________________________________________________________________________

Determine if each conjecture is valid by the Law of Detachment.

3. Given: If m ABC m CBD, then BC bisects ABD.BC bisects ABD. Conjecture: m ABC m CBD. ____________________ 4. Given: You will catch a catfish if you use stink bait. Stuart caught a catfish. Conjecture: Stuart used stink bait. ____________________ 5. Given: An obtuse triangle has two acute angles. Triangle ABC is obtuse. Conjecture: Triangle ABC has two acute angles. ____________________

Determine if each conjecture is valid by the Law of Syllogism. 6. Given: If the gossip said it, then it must be true. If it is true, then

somebody is in big trouble. Conjecture: Somebody is in big trouble because the gossip said it. ____________________ 7. Given: No human is immortal. Fido the dog is not human. Conjecture: Fido the dog is immortal. ____________________ 8. Given: The radio is distracting when I am studying. If it is 7:30 P.M.

on a weeknight, I am studying. Conjecture: If it is 7:30 P.M. on a weeknight, the radio is distracting. ____________________

Draw a conclusion from the given information. 9. Given: If two segments intersect, then they are not parallel. If two segments are

not parallel, then they could be perpendicular. andEF MN intersect.

_________________________________________________________________________________________

10. Given: When you are relaxed, your blood pressure is relatively low. If you are sailing, you are relaxed. Becky is sailing.

_________________________________________________________________________________________

LESSON

x-x

2-202-20

LESSON

2-3


Name ________________________________________ Date __________________ Class__________________



Practice B Algebraic Proof

Solve each equation. Show all your steps and write a justification for each step.

1. 15

(a 10) 3 2. t 6.5 3t 1.3

3. The formula for the perimeter P of a rectangle with length A and width w is

P 2(A w). Find the length of the rectangle shown here if the perimeter is 9 12

feet.

Solve the equation for A and justify each step.

Write a justification for each step.

4.

HJ HI IJ ___________________

7x 3 (2x 6) (3x 3) ___________________

7x 3 5x 3 ___________________

7x 5x 6 ___________________

2x 6 ___________________

x 3 ___________________

Identify the property that justifies each statement. 5. m n, so n m. 6. ABC ABC

_________________________________________ ________________________________________

7. KL LK 8. p q and q 1, so p 1.

_________________________________________ ________________________________________

LESSON

x-x

2-362-36

LESSON

2-5


Name ________________________________________ Date __________________ Class__________________





1. 15

(a 10) 3 2. t 6.5 3t 1.3



feet.



4.

HJ HI IJ ___________________

7x 3 (2x 6) (3x 3) ___________________

7x 3 5x 3 ___________________

7x 5x 6 ___________________

2x 6 ___________________

x 3 ___________________


_________________________________________ ________________________________________


_________________________________________ ________________________________________

LESSON

x-x

2-362-36

LESSON

2-5


Name ________________________________________ Date __________________ Class__________________





1. 15

(a 10) 3 2. t 6.5 3t 1.3



feet.



4.

HJ HI IJ ___________________

7x 3 (2x 6) (3x 3) ___________________

7x 3 5x 3 ___________________

7x 5x 6 ___________________

2x 6 ___________________

x 3 ___________________


_________________________________________ ________________________________________


_________________________________________ ________________________________________

LESSON

x-x

2-362-36

LESSON

2-5


Name ________________________________________ Date __________________ Class__________________





1. 15

(a 10) 3 2. t 6.5 3t 1.3



feet.



4.

HJ HI IJ ___________________

7x 3 (2x 6) (3x 3) ___________________

7x 3 5x 3 ___________________

7x 5x 6 ___________________

2x 6 ___________________

x 3 ___________________


_________________________________________ ________________________________________


_________________________________________ ________________________________________

LESSON

x-x

2-362-36

LESSON

2-5


Nam

e________________________________________

Date

__________________ C

lass__________________

Original content C

opyright © by H

olt McD

ougal. Additions and changes to the original content are the responsibility of the instructor.

Holt M

cDougal G

eometry

Practice B

Algebraic Proof

Solve each equation. Show all your steps and w

rite a justification for each step.

1. 15

(a 10)

3

2. t 6.5

3t 1.3

3. The formula for the perim

eter P of a rectangle w

ith length A and width w

is

P 2( A

w). Find the length of the rectangle show

n here if the perimeter is 9

12 feet.



4.

HJ

HI

IJ ___________________

7x

3 (2x

6) (3x

3) ___________________

7x

3 5x

3 ___________________

7x

5x 6

___________________

2x

6 ___________________

x

3 ___________________

Identify the property that justifies each statement.

5. m

n, so n m

. 6.

ABC

ABC

_________________________________________ ________________________________________

7. KL

LK

8. p q and q

1, so p

1.

_________________________________________ ________________________________________

LESSON

x-x

2-3

62

-36

LESSON

2-5

CS

10_G_M

EC

R710617_C

02L05b.indd 364/8/11 9:37:52 A

M

Minutes-‐Degrees-‐Seconds a. Find the complement of ∠B if m∠B = 49˚57’30’’ b. 124˚25’41’’ – 88˚37’55’’ Clock problems: Find the measure of the angle between the minute and hour hands of the following times: 3:50 1:35 8:15 Proofs

prove

prove

prove

Drawing conclusions: 12.

13.

14. 15.

16.

Documents

Chapter Foundations for Geometry - Mr. Caronna's ...caronnaclassroom.weebly.com/uploads/1/3/3/8/13388109/gh...Which names a pair of opposite rays? A AB JJJG and BG JJJG C AB JJJG and