practice4 answer key

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Chapter 1: Tools of Geometry

Chapter 2: Reasoning and Proof

Chapter 3: Parallel and Perpendicular Lines

Chapter 4: Congruent Triangles

Chapter 5: Relationships Within Triangles

Chapter 6: Quadrilaterals

Chapter 7: Similarity

Chapter 8: Right Triangles and Trigonometry

Chapter 9: Transformations

Chapter 10: Area

Chapter 11: Surface Area and Volume

Chapter 12: Circles


Tools of Geometry

1. Identify the ray that is the opposite of.

2. Which segment is NOT skew to segment?

3. The complement of an angle is 29. What is the measure of the angle?

61

29

151

149

4.bisects RST. Find the measure of RST if mQST = 45.


40

100

45

90

5. In the figure shown, mAED = 97. Which statement is false?

mAEB = 83

mBEC = 97

AEB and mDEC are congruent angles.

BEC and mCED are vertical angles.

6. a. If EF = 5w + 28, FG = 7w + 20, and EG = 36, find the value of w. b. Find EF and FG.

a. w = 2; b. EF = 38, FG = 34

a. w = 1; b. EF = 23, FG = 13

a. w = 4; b. EF = 48, FG = 48

a. w = 3; b. EF = 43, FG = 41

7. What is the next term in the sequence? 4, 7, 10, 13, .

16

10

14

19

8. Anita is practicing to join the swim team. The first time she timed her lap it was 1 minute and 12 seconds. After one week of practice, her best lap was 1 minute and 9 seconds. After a second week of practice, her best lap was 1 minute and 6 seconds. Use inductive reasoning to predict how long her best lap will be after 3 weeks of practice.

1 minute 3 seconds


1 minute 9 seconds

1 minute 6 seconds

1 minute 5 seconds

9. The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the _____ of the _____ of the corresponding numbers.

product, absolute values

absolute value, difference

difference, values

sum, squares

10. Which is an incorrect way to name the line?

line t

11. If two lines intersect, then they intersect in exactly _____.

one point

one line

two points

one plane

12. Determine the coordinates of the midpoint ofand find the distance EB for the points E(3, 3) and B(2, 2).

midpoint = ( ,

midpoint = ( ,

midpoint = ( ,

midpoint = ( ,

); distance =

); distance = 5

); distance = 5

); distance =


13. If mDOE = 23 and mCOD = 20, then what is the measure of COE?

40

45

48

43

14. Find AC and BD.

AC = 10; BD = 2

AC = 11; BD = 3

AC = 3; BD = 11

AC = 11; BD = 3

15. May's Internet Services designs Web sites. May noticed an increase in her customers over a period of 5 consecutive weeks. The first week she had 1 customer, the second week she had 3 customers, and the third week she had 5 customers. Use inductive reasoning to make a conjecture about the number of customers May will have in the sixth week.

10

12

9

11

16. Which drawing shows a three-dimensional figure sketched from these views?


17. If AB = 19 and BC = 3, then AC = _____?

19

25

22

16

18. A highway map of Ohio has a coordinate grid superi mposed on top of the state. Springfield is at point (1, 4) and Columbus is at point (7, 1). The Springfield youth soccer team is going to Columbus to see a professional soccer match. The map shows a highway rest area halfway between the cities. What are the coordinates of the rest area? What is the distance between Springfield and Columbus? (one unit = 5.38 miles)

Rest area = (3,); distance = 40 miles

Rest area = (3,); distance = 46 miles


Rest area = ( , 4); distance = 18 miles

Rest area = (4, ); distance = 42 miles

19. Write a formula that will give the area of the shaded region in the figure below.

A = (29 12) (3 2)

A = (29 3) (12 2)

A = 29 12

A = (29 2) (123)

20. Noam walks home (8, 4) from school (2, 4) by walking 8 blocks north, then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house?

14 blocks

4 blocks

10 blocks

The distance would be the same.


Tools of Geometry

1. Identify the ray that is the opposite of.

CORRECT:

2. Find the coordinates of the midpoint of the segment connecting H(6, 0) andK(8, 14).

CORRECT: (1, 7)

3. Name an angle complementary to COD.

CORRECT: BOC

4. If AB = 19 and BC = 3, then AC = _____?

CORRECT: 22

5. Which point is NOT colinear with two other points?

CORRECT: A


6. Which drawing shows a three-dimensional figure sketched from these views?

CORRECT:

7. Anita is practicing to join the swim team. The first time she timed her lap it was 1 minute and 12 seconds. After one week of practice, her best lap was 1 minute and 9 seconds. After a second week of practice, her best lap was 1 minute and 6 seconds. Use inductive reasoning to predict how long her best lap will be after 3 weeks of practice.

CORRECT: 1 minute 3 seconds

8. What is the first step in constructing a congruent segment?

CORRECT: Draw a ray.

9. In the figure shown, name the ray that appears to bisect JKL.

CORRECT:

10. If KM = 305, and KL = 3x + 2, and LM = 5x 1, find the value of x. Then findKL and LM.

CORRECT: x = 38, KL = 116, LM = 189

11. Ralph wants to put up a fence around his rectangular garden, which measures 48 feet by 54 feet. He wants to include the path around it on two sides that is 3 feet wide. How much fencing material does he need?

CORRECT: 216 ft

12. Supplementary angles are two angles whose measures have sum _____. Complementary angles are two angles whose measures have sum _____.


CORRECT: 180; 90

13. The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the _____ of the _____ of the corresponding numbers.

CORRECT: absolute value, difference 14. Which figure is a net for a cube?

CORRECT:

15. Which of these points, if any, is the midpoint of?

CORRECT: none of them

16. a. If EF = 5w + 28, FG = 7w + 20, and EG = 36, find the value of w. b. Find EF and FG.

CORRECT: a. w = 1; b. EF = 23, FG = 13

17. Which of the following describes the figure below?

CORRECT:

18. Find AB and BC. Are AB and BC congruent?

CORRECT: AB = 3; BC =2 ; no, they are not congruent 19. What is the next term in the sequence? 4, 7, 10, 13, .

CORRECT: 16

20. If two planes intersect, then they intersect in exactly _____.

CORRECT: one line

.


Reasoning and Proof

1. Which of the following choices shows a true conditional with the hypothesis and conclusion identified correctly?

If yesterday was Saturday, then tomorrow is Monday. hypothesis: Yesterday was Saturday.conclusion: Tomorrow is Monday.

If yesterday was Saturday, then tomorrow is Monday. hypothesis: Tomorrow is Monday.conclusion: Yesterday was Saturday.

If yesterday was Saturday, then today is Monday. hypothesis: Yesterday was Saturday.conclusion: Tomorrow is Monday.

If yesterday was Saturday, then today is Monday. hypothesis: Tomorrow is Monday.conclusion: Yesterday was Saturday.

2. Select the appropriate property of equality for the statement. If a = b, then b= a.

Addition Property

Symmetric Property

Transitive Property

Substitution Property

3. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the given statements.Franz is taller than Isabel. Isabel is shorter than Ellen. Janina is taller than Franz.

Janina is shortest.

Janina is taller than Isabel.

Franz is the tallest.

Ellen is shorter than Isabel.

4. Determine if the conditional and its converse are true. If they are both true, select which biconditional correctly represents them. If either the conditional or the converse is false, select the counterexample which disproves the statement:If four points are non-coplanar, then they are non-collinear. If four points are non-collinear, then they are non-coplanar.

Counterexample: If four points are non-coplanar, they still may be collinear.

If and only if four points are non-collinear are they non-coplanar.

Four points are non-coplanar if and only if they are non-collinear.


Counterexample: Four points may be non-collinear and yet lie in the same plane.

5. Is it possible to use the Law of Detachment to draw a conclusion?

I will go to the cinema if and only if I can afford to buy a ticket. The movie starts at 7:30.

Yes, it is possible.

No, it is not possible.

6. One way to show that a statement is NOT a good defi nition is to find a _____.

biconditional

conditional

converse

counterexample

7. Which of the following is an example of the Reflexive Property of Equality?

If x = 2, then x + 4 = 2 + 4.

x 2 = x 2

If y = x + 4, then x + 4 = y.

If x 2 = y and y = 4, then x 2 = 4. 8. Find the value of the variable.

2

3

4

5

9. Is the converse of the true statement also true?

If four points are non-coplanar, then they are non-collinear.

Yes, it is true.

No, it is false.


10. Which biconditional is a good definition?

segment.

Two angles are adjacent if and only if they share a common side.

A point is the midpoint of a segment if and only if it is between the endpoints of the

Two angles are supplementary if and only if they form a linear pair.

Two lines are parallel if and only if they never intersect.

11. Two angles whose sides are opposite rays are called _____. Two coplanar angles with a common side, a common vertex, and no common interior points are called _____.

adjacent angles; vertical angles

vertical angles; adjacent angles

adjacent angles; complementary angles

vertical angles; supplementary angles

12. Which is the converse of this conditional? If it is appropriate, then I play golf.

If it is appropriate, then I do not play golf.

If I play golf, then it is appropriate.

If I do not play golf, then it is appropriate.

If it is not appropriate, then I play golf. 13. Which is the Law of Syllogism in symbolic form?

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

If p q is a true statement and p is true, then q is true.

If p q and q r are false statements, then p r is a false statement.

If p q is a false statement and p is false, then q is false.

14. Decide if the statement is reversible. If so, identify the true biconditional. Two lines that intersect at right angles are perpendicular.

If two lines intersect at right angles, then they are not perpendicular.

If two lines intersect at right angles, then they are perpendicular.

Two lines intersect at right angles if and only if they are perpendicular.

not reversible


15. Identify the converse of the conditional statement. Determine the truth values of the original conditional and its converse. If an angle is a right angle, then its measure is 90.

If the measure of an angle is 90, then it is a right angle. original: trueconverse: true

If an angle is not a right angle, then its measure is not 90. original: trueconverse: true

If an angle is not a right angle, then its measure is 90. original: trueconverse: false

If the measure of an angle is 90, then it is a right angle. original: trueconverse: false

16. Complete the proof.

Given: A and B are right angles. Prove: A B

By the definition of a. _____, mA = 90 and mB = 90. By the b. _____ Property,mA = mB or A _ B.

a. complementary angles b. Substitution

a. right angles b. Reflexive

a. right angles b. Distributive

a. right angles b. Substitution

17. What is the conclusion of the following statement? "A number is even if the number is divisible by 6."

A number is even if the number is divisible by 6.

A number is divisible by 6 if the number is even.

A number is divisible by 6.

The number is even.


18. Find the value of the variables.

x = 29, y = 60

x = 26, y = 30

x = 26, y = 60

x = 29, y = 30

19. Find the value of the variable.

6

3

5

8

20. Supply the missing step in the following proof. Given: 4x 6y = 8; x = 10Prove: 8 = y

6y = 32; Multiplication Property of Equality

6y = 48; Subtraction Property of Equality

6y =48; Multiplication Property of Equality

6y = 32; Subtraction Property of Equality


Reasoning and Proof

1. Which of the following is an example of the Reflexive Property of Equality?

CORRECT: x 2 = x 2

2. Is the following statement reversible?

If two angles are adjacent, then they share a common side.

CORRECT: No, it is not reversible.

3. Which is a counterexample to the following faulty definition? A square is a figure with four congruent sides.

CORRECT: A rhombus has four congruent sides. 4. Find the value of the variable.

CORRECT: 4

5. Which is a counterexample that proves this conditional is false? All prime numbers are odd.

CORRECT: 2

6. Which biconditional is a good definition?

CORRECT: Two angles are adjacent if and only if they share a common side.

7. Identify the converse of the conditional statement. Determine the truth values of the original conditional and its converse. If an angle is a right angle, then its measure is 90.

original: true converse: trueCORRECT: If the measure of an angle is 90, then it is a right angle. original: trueconverse: true

8. Select the appropriate property of equality for the statement. If a = b, then a c = b c.

CORRECT: Multiplication Property


9. In the figure shown, mAED = 97. Which statement is false?

CORRECT: BEC and mCED are vertical angles.

10. Select the appropriate property of equality for the statement. If a = b, then b= a.

CORRECT: Symmetric Property

11. Select the appropriate property of equality for the statement a = a.

CORRECT: Reflexive Property

12. A conditional can have a _____ of true or false.

CORRECT: truth value

13. Which is the converse of this conditional? If it is appropriate, then I go for a drive.

CORRECT: If I go for a drive, then it is appropriate.

14. Use the Law of Syllogism to draw a conclusion.

If a country's population is more than 1.033 billion, then it has a higher population than India. If a country has a higher population than India, then it is has the highest population in the world.

CORRECT: If a country's population is more than 1.033 billion, then it is has the highest population in the world.

15. The complement of an angle is 29. What is the measure of the angle?

CORRECT: 61

16. Name an angle complementary to COD.

CORRECT: BOC

17. Decide if the statement is reversible. If so, identify the true biconditional. Two lines that intersect at right angles are perpendicular.

CORRECT: Two lines intersect at right angles if and only if they are perpendicular.


18. One way to show that a statement is NOT a good d efinition is to find a _____.

CORRECT: counterexample

19. Which is the converse of this conditional? If it is a dog, then it is a pet.

CORRECT: If it is a pet, then it is a dog.

20. Use the Law of Syllogism to draw a conclusion.

If a substance is water, then its molecular structure is H2O. If a substance has molecular structure H2O, then its boiling point at sea level is 100C.

CORRECT: If a substance is water, then its boiling point at sea level is 100C.

Parallel and Perpendicular Lines

1. If c b and a || c, what is m2?

60

90

30

not enough information

2. Which is an equation in slope-intercept form of the line that contains the pointsS(7, 9) and T(8, 7)?

y = 2x 23

x + 2y = 23

x 2y = 23

y = 2x + 23


3. Find the value of x for a to be parallel to b.

4. An irregular quadrilateral has exterior angle measures of 93, 85, and 89. What is the measure of the fourth interior angle?

273

267

93

87

5. How many sides does a regular polygon have if each exterior angle measures 12?

24

168

30

none of these

6. Find the slope of a line parallel to the graph of 4x 2y = 9.

2

2


7. Which of the following statements is true?

ABH and DEF are alternate interior angles.

BED and EBH are same-side interior angles.

ABC and BED are alternate interior angles.

CBE and DEF are corresponding angles.

8. Find the slope of a line parallel to the line containing the points A(2, 7) andB(8, 9).

5

0.5

2

9. Below is a diagram of an airport runway intersection. There are two parallel runways, and a taxiway crosses both runways. If 8 measures 115 what is the sum of 1 and 4?

130

65

230

115


10. Which are corresponding angles?

6 and 16

1 and 12

8 and 16

none of these

11. Find the value of the variable. The diagram is NOT to scale.

SRT _ STR SRT = 30 STU = 9x

2

7

16

none of these

12. Construct a perpendicular from the given line segment that passes through the given point.


none of these

13. Which drawing is a construction of the perpendicular line tofrom S?


14. Which algebraic expression is equivalent to 3x(xN + 2) + 2(x + 1)?

3xO + 2x + 8

3xN + 2x + 8

3xO + 8x + 2

3xN + 8x + 2

15. Which is a correct name for the polygon?

BADEC

ABEDC

EDABC

CDEAB


16. Using the given information, which lines, if any, can you conclude are parallel? Justify your conclusion with a theorem or postulate. m1 + m2 = 180

g || h by the Converse of the Alternate Interior Angles Theorem

g || h by the Converse of the Same-Side Interior Angles Theorem

j || k by the Converse of the Alternate Interior Angles Theorem

j || k by the Converse of the Same-Side Interior Angles Theorem 17. Classify the triangle with sides of lengths 23, 23, and 21.

scalene

isosceles

straight

equilateral

18. Find the value of the variable if m || l, m3 = 2x + 106, and m4 = 4x + 38.

5

6

4

7


19. Which of the equations is a line parallel to 4x 2y = 7?

2y = 4x + 7

4x 2y = 7

2y = 4x + 2

4x + 2y = 2

20. Which diagram shows the correct construction of a line parallel to line l and passing through point P?


Parallel and Perpendicular Lines

1. If c b and a || c, what is m2?

CORRECT: 90

2. Which is an equation in slope-intercept form of the line that contains the pointsS(7, 9) and T(8, 7)?

CORRECT: y = 2x 23

3. Find the value of x for a to be parallel to b.

CORRECT:

4. An irregular quadrilateral has exterior angle measures of 93, 85, and 89. What is the measure of the fourth interior angle?

CORRECT: 87

5. How many sides does a regular polygon have if each exterior angle measures 12?

CORRECT: 30

6. Find the slope of a line parallel to the graph of 4x 2y = 9.

CORRECT: 2

7. Which of the following statements is true?


CORRECT: CBE and DEF are corresponding angles.

8. Find the slope of a line parallel to the line containing the points A(2, 7) andB(8, 9).

CORRECT:

9. Below is a diagram of an airport runway intersection. There are two parallel runways, and a taxiway crosses both runways. If 8 measures 115 what is the sum of 1 and 4?

CORRECT: 230

10. Which are corresponding angles?

CORRECT: 8 and 16

11. Find the value of the variable. The diagram is NOT to scale.

SRT _ STR SRT = 30 STU = 9x

CORRECT: 16

12. Construct a perpendicular from the given line segment that passes through the given point.


CORRECT:

13. Which drawing is a construction of the perpendicular line tofrom S?

CORRECT:

14. Which algebraic expression is equivalent to 3x(xN + 2) + 2(x + 1)?

CORRECT: 3xO + 8x + 2

15. Which is a correct name for the polygon?

CORRECT: CDEAB


16. Using the given information, which lines, if any, can you conclude are parallel? Justify your conclusion with a theorem or postulate. m1 + m2 = 180

CORRECT: j || k by the Converse of the Same-Side Interior Angles Theorem

17. Classify the triangle with sides of lengths 23, 23, and 21.

CORRECT: isosceles

18. Find the value of the variable if m || l, m3 = 2x + 106, and m4 = 4x + 38.

CORRECT: 6

19. Which of the equations is a line parallel to 4x 2y = 7?

CORRECT: 2y = 4x + 7

20. Which diagram shows the correct construction of a line parallel to line l and passing through point P?

CORRECT:


Congruent Triangles

1. Use the information given in the diagram. Tell why each statement is true. a._b._

a. given; b. Reflexive Property

a. Reflexive Property; b. given

a. Reflexive Property; b. Transitive Property

a. Transitive Property; b. Reflexive Property

2. Is ABD _ CBD by HL? If so, state the leg(s) that allows the use of HL.

no

yes,and

yes,

yes,and

3. ABCD is an isosceles trapezoid, and_. Which statement is NOT true?

ABY _ BAX

_

_

DXB _ DYB



Given:_and_. Prove: FAC _ EDB.

def. of congruent triangles

SSS

SAS

none of these

5. The two triangles are congruent. Find the missing side lengths and the missing angle measures.

d = 5 m; e = 32; f = 90; g = 58; h = 5 m

d = 8 m; e = 32; f = 90; g = 58; h = 9.4 m

d = 5 m; e = 32; f = 90; g = 58; h = 9.4 m

d = 5 m; e = 32; f = 58; g = 90; h = 5 m



Given:bisects URS andbisects UTS. Prove: URT _ SRT.

Reflexive property

definition of angle bisector

HL Theorem

CPCTC


Given:bisects EBC andbisects ECC. Prove:EBD _ CBD.


Same-Side Interior Angles Theorem

given

SSS postulate

Triangle Inequality Theorem

8. Given that EAC _ ECA, which other information would NOT help you prove th at_?

B _ D

_

_

_

9. Given QRS _ TUV, find the measure of the given angles and the lengths of the given sides. a. QS = 3v + 1, TV = 5v 9

b. mR = 4n + 4, mU = 5n 4

a. 16; b. 32

a. 5; b. 8

a. 16; b. 36

a. 8; b. 32

10. Given_and_, use the coordinates of A, B, F, and E to proveB _ E.

By adding DC to both AD and FC, which are equal,_. Because AB ==FE,_. So, by (a)_____, ABC _ FED, and then B _ E by (b)_____.

a. SAS; b. CPCTC

a. SSS; b. SAS


a. ASA; b. HL

a. SSS; b. CPCTC

11. From the information in the diagram, can you prove that FDG and FDE are congruent? Explain.

yes; AAA

yes; ASA

yes; SSS

no

12. What is the measure of each base angle of an isosceles triangle if its third angle measures 32 degrees and its 2 congruent sides measure 15 units?

32

74

148

58

13. Why is ADB _ CDB?

SAS


SSS

neither of these

They are not congruent.

14. Use information in the figure below to find mD.

11.75

47

94

23.5

15. What else must you know to prove the triangles congruent for the reason shown? a. ASAb. SAS

a. ADC _ ABC; b._

a. ACD _ CAB; b._

a. ACD _ CAB; b._

a._; b. ACD _ CAB

16. Given DEF, if_and mE = 30, which is the measure of F?

90

75

60

30



Given:_, BAD _ CAD. Prove: andbisects.

a. ASA; b. CPCTC

a. SSS; b. Reflexive Property

a. SAS; b. Reflexive Property

a. SAS; b. CPCTC

18. Is ABD _ CBD by HL? If so, state the leg that allows the use of HL.

yes,

no

yes,and

yes,and


19. In which triangles could you efficiently prove 1 _ 2 using the HL Theorem?

II only

III only

II and III

I only

20. ABD _ CBD. Name the theorem or postulate that justifies the congruence.

ASA

SAS

AAS

none of these

Congruent Triangles

1. Use the information given in the diagram. Tell why each statement is true. a._b._

CORRECT: a. Reflexive Property; b. given


2. Is ABD _ CBD by HL? If so, state the leg(s) that allows the use of HL.

CORRECT: yes,

3. ABCD is an isosceles trapezoid, and_. Which statement is NOT true?

CORRECT: DXB _ DYB 4. Complete the proof.Given:_and_. Prove: FAC _ EDB.

CORRECT: SAS

5. The two triangles are congruent. Find the missing side lengths and the missing angle measures.

CORRECT: d = 5 m; e = 32; f = 90; g = 58; h = 9.4 m 6. Complete the proof.Given:bisects URS andbisects UTS. Prove: URT _ SRT.


CORRECT: definition of angle bisector 7. Complete the proof.Given:bisects EBC andbisects ECC. Prove:EBD _ CBD.

CORRECT: given

8. Given that EAC _ ECA, which other information would NOT help you prove th at_?

CORRECT:_


9. Given QRS _ TUV, find the measure of the given angles and the lengths of the given sides. a. QS = 3v + 1, TV = 5v 9

b. mR = 4n + 4, mU = 5n 4

CORRECT: a. 16; b. 36

10. Given_and_, use the coordinates of A, B, F, and E to proveB _ E.

By adding DC to both AD and FC, which are equal,_. Because AB ==FE,_. So, by (a)_____, ABC _ FED, and then B _ E by (b)_____.

CORRECT: a. SSS; b. CPCTC

11. From the information in the diagram, can you prove that FDG and FDE are congruent? Explain.

CORRECT: yes; ASA

12. What is the measure of each base angle of an isosceles triangle if its third angle measures 32 degrees and its 2 congruent sides measure 15 units?

CORRECT: 74


13. Why is ADB _ CDB?

CORRECT: SAS

14. Use information in the figure below to find mD.

CORRECT: 23.5

15. What else must you know to prove the triangles congruent for the reason shown? a. ASAb. SAS

CORRECT: a. ACD _ CAB; b._

16. Given DEF, if_and mE = 30, which is the measure of F?

CORRECT: 75 17. Complete the proof.Given:_, BAD _ CAD. Prove: andbisects.


CORRECT: a. SAS; b. CPCTC

18. Is ABD _ CBD by HL? If so, state the leg that allows the use of HL.

CORRECT: no

19. In which triangles could you efficiently prove 1 _ 2 using the HL Theorem?

CORRECT: III only

20. ABD _ CBD. Name the theorem or postulate that justifies the congruence.


CORRECT: SAS

Relationships Within Triangles

1. Which lengths could be the sides of a triangle?

8 cm, 17 cm, 9 cm

22 cm, 12 cm, 9 cm

17 cm, 8 cm, 10 cm

12 cm, 22 cm, 8 cm

2. Points B, D, and F are midpoints of the sides of ACE. EC = 40 and DF = 18. a. Find AC.b. Find FB.

a. 80; b. 9

a. 36; b. 20

a. 20; b. 18

a. 20; b. 36

3. List the sides of ABC in order from shortest to longest, when mA = 10x 7,mB = 7x 10, and mC = 47 2x.

;;

;;

;;

;;


4. Write the conditional statement illustrated by the Venn diagram.

If an animal is not a cow, then it is not a mammal.

If an animal is a mammal, then it is a cow.

If an animal is a cow, then it is a mammal.

If an animal is not a mammal, then it is not a cow. 5. Write the side lengths from least to greatest.

,,

,,

,,

,,

6. Which pair of statements has the same truth value?

the inverse and converse of a conditional statement

the converse and the contrapositive of a conditional statement

a conditional statement and its inverse

a conditional statement and its converse

7. Find the inverse of the statement "If she is not tall, she will not make the basketball team."

If she is tall, she will not make the basketball team.

If she will not make the basketball team, she is tall.

If she is tall, she will make the basketball team.

If she is not tall, she will make the basketball team.


8.andare perpendicular bisectors of each other. a. Find DC.b. Find DB. c. Find AE.

a. 13; b. 24; c. 5

a. 13; b. 24; c. 10

a. 13; b. 12; c. 5

a. 13; b. 12; c. 10 9. Find FG.

12

4

19

15


;;

;;

;;

;;


11. Given:is the perpendicular bisector of. What can you NOT conclude?

JMP, KMP, KMO, and JMO are rt s.

M is the midpoint of.

M is the midpoint of.

_

12. Name the second largest angle in the figure if the side between 1 and 2 is 14 cm, the side between 2 and 3 is 15 cm, and the side between 3 and 1 is 18 cm. (not drawn to scale)

2

1

3

4

13. Given:is the perpendicular bisector of. Which statement is true?

E is the midpoint of.

HDJ is a right angle.

EJ = DJ


14. Find the value of x.

14

7

11.5

9

15. Determine which three lengths can be measures of the sides of a triangle.

10 cm, 4 cm, 13 cm

3 cm, 10 cm, 13 cm

15 cm, 3 cm, 19 cm

2 cm, 15 cm, 19 cm

16. Find mQST.

7.5

75

15

30


17. B is the midpoint of, D is the midpoint of, and BD = 7. Find AE.

7

14

49

21

18. Given:is the bisector of. What can you NOT conclude?

L is the midpoint of.

CLM, MLD, DLK, and KLC are rt s.

_

19. Find the length ofgiven thatis a median of the triangle and BC is 20.

40

10

20


21

20. Identify the segment interior to the triangle with respect to the whole figure.

midsegment

perpendicular bisector

altitude

angle bisector

Relationships Within Triangles

1. Which lengths could be the sides of a triangle?

CORRECT: 17 cm, 8 cm, 10 cm

2. Points B, D, and F are midpoints of the sides of ACE. EC = 40 and DF = 18. a. Find AC.b. Find FB.

CORRECT: a. 36; b. 20


CORRECT:;;


4. Write the conditional statement illustrated by the Venn diagram.

CORRECT: If an animal is a cow, then it is a mammal. 5. Write the side lengths from least to greatest.

CORRECT:,,

6. Which pair of statements has the same truth value?

CORRECT: the inverse and converse of a conditional statement

7. Find the inverse of the statement "If she is not tall, she will not make the basketball team."

CORRECT: If she is tall, she will make the basketball team.

8.andare perpendicular bisectors of each other. a. Find DC.b. Find DB. c. Find AE.

CORRECT: a. 13; b. 24; c. 5 9. Find FG.


CORRECT: 15


CORRECT:;;

11. Given:is the perpendicular bisector of. What can you NOT conclude?

CORRECT: M is the midpoint of.

12. Name the second largest angle in the figure if the side between 1 and 2 is 14 cm, the side between 2 and 3 is 15 cm, and the side between 3 and 1 is 18 cm. (not drawn to scale)

CORRECT: 2

13. Given:is the perpendicular bisector of. Which statement is true?

CORRECT: 14. Find the value of x.

CORRECT: 7


15. Determine which three lengths can be measures of the sides of a triangle.

CORRECT: 10 cm, 4 cm, 13 cm

16. Find mQST.

CORRECT: 15

17. B is the midpoint of, D is the midpoint of, and BD = 7. Find AE.

CORRECT: 14

19. Find the length ofgiven thatis a median of the triangle and BC is 20.

CORRECT: 20

20. Identify the segment interior to the triangle with respect to the whole figure.

CORRECT: angle bisector


Part 2/2

practice4 answer key

Documents

area chapter

proof chapter

volume chapter

quadrilaterals chapter

trigonometry chapter

transformations chapter

similarity chapter

congruent triangles