Extra Practice - Mrs. Sevilla's Math...

Extra Practice

CHAPTER 1

Describe a pattern in the sequence of numbers. Predict the next number. (Lesson 1.1)

1. 16, 8, 4, 2, 1, . . . 2. 1, 2, 4, 7, 11, . . . 3. 1, 5, 25, 125, . . .

4. 7, 2, 2, 8, 2, 2, 9, 2, 2, . . . 5. 32, 48, 72, 108, . . . 6. 2, º6, 18, º54, . . .

7. Complete the conjecture based on the pattern you observe in the specificcases. (Lesson 1.1)Conjecture: Any negative number cubed is !!!!!?!!!.

º13 = º1 º73 = º343º33 = º27 º93 = º729º53 = º125 º113 = º1331

8. Show that nn + 1 > (n + 1)n for the values n = 3, 4, and 5. Then show thatthe values n = 1 and n = 2 are counterexamples to the conjecture that nn + 1 > (n + 1)n. (Lesson 1.1)

Sketch the points, lines, segments, planes, and rays. (Lesson 1.2)

9. Draw four collinear points A, B, C, and D.

10. Draw two opposite rays MNÆ̆

and MPÆ̆

.

11. Draw a plane that contains two intersecting lines.

12. Draw three points E, F, and G that are coplanar, but are not collinear.

13. Draw two points, R and S. Then sketch RSÆ̆

. Add a point T on the ray so thatS is between R and T.

In the diagram of the collinear points, AE = 24, C is the midpoint of AEÆ

, AB = 8, and DE = 5. Find each length. (Lesson 1.3)

14. BC 15. AD

16. BD 17. AC

18. CD 19. BE

Use the Distance Formula to decide whether HMÆ

£ MLÆ

. (Lesson 1.3)

20. H(º1, 3) 21. H(3, º1) 22. H(º5, 2)M(1, 7) M(8, 2) M(º4, 6)L(3, 3) L(3, 5) L(º6, 2)

Name the vertex and sides of the angle, then write two names for the angle. (Lesson 1.4)

23. 24. 25.

C

B

A

E

FGP

q

R

Extra Practice 803

A B C D E

http://www.classzone.com

Use the Angle Addition Postulate to find the measure of the unknown angle. (Lesson 1.4)

26. m™STR = !!!!!!?! 27. m™HJK = !!!!!!?! 28. m™DEF = !!!!!!?!

State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure. (Lesson 1.4)

29. 30. 31.

Find the coordinates of the midpoint of a segment with the given endpoints. (Lesson 1.5)

32. P(º4, 2) 33. P(º1, 3.5) 34. P(º12, 4)Q(8, º4) Q(7, º5.5) Q(º3, º6)

XYÆ̆

is the angle bisector of ™UXB. Find m™UXY. (Lesson 1.5)

35. 36. 37.

Find the measure of each angle. (Lesson 1.6)

38. Two vertical angles are complementary. Find the measure of each angle.

39. The measure of one angle of a linear pair is 3 times the measure of the otherangle. Find the measures of the two angles.

40. The supplement of an angle is 130°. Find the complement of the angle.

Find the perimeter (or circumference) and area of the figure. (Where necessary, use π ≈ 3.14.) (Lesson 1.7)

41. 42. 43. 44.

45. 46. 47. 48.

12

9.25

7.2535

18

8

13

13

10123

4

57

U

XY

B

(5z ! 19)"(7z # 3)"

U

XY

B

(4r ! 1)"(3r ! 7)"

U

X

Y

B84"

C

E F

60"150"

D

H

K

J35"30"L

R

TS110"

804 Student Resources


CHAPTER 2

Rewrite the conditional statement in if-then form. (Lesson 2.1)

1. It must be true if you read it in a newspaper.

2. An apple a day keeps the doctor away.

3. The square of an odd number is odd.

Write the inverse, converse, and contrapositive of the conditionalstatement. (Lesson 2.1)

4. If x = 12, then x2 = 144.

5. If you are indoors, then you are not caught in a rainstorm.

6. If four points are collinear, then they are coplanar.

7. If two angles are vertical angles, then they are congruent.

Write the converse of the true statement. Decide whether the converse istrue or false. If false, provide a counterexample. (Lesson 2.1)

8. If two angles form a linear pair, then they are supplementary.

9. If 2x º 5 = 7, then x = 6.

Rewrite the biconditional statement as a conditional statement and itsconverse. (Lesson 2.2)

10. Two segments have the same length if and only if they are congruent.

11. Two angles are right angles if and only if they are supplementary.

12. x = 10 if and only if x2 = 100.

Determine whether the statement can be combined with its converse toform a true biconditional statement. (Lesson 2.2)

13. If ™ABC is a right angle, then A!B! fi B!C!.

14. If ™1 and ™2 are adjacent, supplementary angles, then ™1 and ™2 form alinear pair.

15. If two angles are vertical angles, then they are congruent.

Using p, q, r, and s below, write the symbolic statement in words. (Lesson 2.3)

p : We go shopping. r : We stop at the bank.q : We need a shopping list. s : We see our friends.

16. p ˘ q 17. ~r ˘ ~s 18. r ˘ s

19. p ¯̆ q 20. ~p ˘ ~s 21. p ¯̆ r

Given that the statement is of the form p ˘ q, write p and q. Then write the inverse and the contrapositive of p ˘ q both symbolically and in words. (Lesson 2.3)

22. If it is hot, May will go to the beach.

23. If the hockey team wins the game tonight, they will play in the championship.

24. If John misses the bus, then he will be late for school.

Extra Practice 805


Use the property to complete the statement. (Lesson 2.4)

25. Reflexive property of equality: AB = !!!!!!?! .

26. Symmetric property of equality: If ED = DF, then !!!!!!?! .

27. Transitive property of equality: If AB = AC and AC = DF, then !!!!!!?! .

28. Division property of equality: If 2x = 3y, then !2zx! = !!!!!!?! .

29. Subtraction property of equality: If x = 6, then x º 4 = !!!!!!?! .

Copy and complete the proof using the diagram and the given information. (Lesson 2.5)

30. GIVEN ! PDÆ £ PCÆ,P is the midpoint of ACÆ and BDÆ

PROVE ! APÆ £ BPÆ

In Exercises 31–32, use the diagram to complete the statement. (Lesson 2.6)

31. ™2 and !!!!!?!!! are vertical angles.

32. ™QWR is supplementary to !!!!!?!!!.

33. In the diagram, suppose that ™3 and ™4 are complementary and that ™4 and™5 are complementary. Prove that ™3 £ ™5. (Lesson 2.6)

Solve for each variable. (Lesson 2.6)

34. 35. 36.

37. Write a two-column proof. (Lesson 2.6)

GIVEN ! ™1 and ™4 are complementary,™DBE is a right angle.

PROVE ! ™2 and ™3 are complementary.

(3r ! 44)"(8s # 19)"

(5s ! 11)"(5r # 6)"

(9b # 36)"

(5c ! 9)"(6c # 18)"

(7b # 20)"

(8z ! 12)"(4z ! 12)"

(5x ! 14)"(10x ! 16)"


A B

CD

P

CD

A

B

E

2

34

1

1. P is the midpoint of ACÆ and BDÆ.2. AP = PC3. BP = PD4. !!!!!?!!!

5. PD = PC6. !!!!!?!!!

7. APÆ £ BPÆ

Statements Reasons

1. !!!!!?!!!

2. !!!!!?!!!

3. !!!!!?!!!

4. Given5. !!!!!?!!!

6. Transitive property of equality7. Definition of congruent segments

q

R

ST

P

U

VW

23

456

7


CHAPTER 3

Think of each segment in the diagram as part of a line. Fill in the blank with parallel, skew, or perpendicular. (Lesson 3.1)

1. HA¯̆

and EC¯̆

are !!!!!?!!!.

2. FD¯̆

and AD¯̆

are !!!!!?!!!.

3. AD¯̆

and GB¯̆

are !!!!!?!!!.

Think of each segment in the diagram as part of a line. There may be more than one right answer. (Lesson 3.1)

4. Name a line parallel to AD¯̆

.

5. Name a line perpendicular to GB¯̆

.

6. Name a line skew to EC¯̆

.

7. Name a plane parallel to GBC.

Complete the statement with corresponding, alternate interior, alternate exterior, or consecutive interior. (Lesson 3.1)

8. ™3 and ™7 are !!!!!?!!! angles.

9. ™4 and ™6 are !!!!!?!!! angles.

10. ™8 and ™2 are !!!!!?!!! angles.

11. ™4 and ™5 are !!!!!?!!! angles.

12. ™5 and ™1 are !!!!!?!!! angles.

13. Fill in the blanks to complete the proof. (Lesson 3.2)

GIVEN ! ABÆ fi BCÆ,BDÆ̆

bisects ™ABC

PROVE ! m™ABD = 45°

Extra Practice 807

A D

C

EG

H F

B

7 86 5

3 42 1

B C

AD

1. ABÆ fi BCÆ

2. !!!!!?!!!

3. m™ABC = 90°4. BD

Æ̆ bisects ™ABC

5. m™ABD = m™DBC6. m™ABD + m™DBC = 90°7. m™ABD + !!!!!?!!! = 90°8. 2(m™ABD) = 90°9. m™ABD = 45°

Statements Reasons

1. !!!!!?!!!

2. Definition of perpendicular lines3. !!!!!?!!!

4. !!!!!?!!!

5. !!!!!?!!!

6. !!!!!?!!!

7. Substitution property of equality8. !!!!!?!!!

9. !!!!!?!!!


Find the values of x and y. Explain your reasoning. (Lesson 3.3)

14. 15. 16.

17. 18. 19.

Which lines, if any, are parallel? Explain. (Lesson 3.4)

20. 21. 22.

Explain how you would show that a ∞ b. State any theorems or postulatesthat you would use. (Lesson 3.5)

23. 24. 25.

Find the slopes of AB¯̆

, CD¯̆

, and EF¯̆

. Which lines are parallel, if any? (Lesson 3.6)

26. A(3, 7), B(1, 5) 27. A(º4, 1), B(3, 1) 28. A(º3, 2), B(º3, 5)C(4, 1), D(9, 6) C(º2, º1), D(4, º3) C(7, º1), D(7, 7)E(2, 5), F(º8, º5) E(º10, 3), F(4, º8) E(4, º11), F(4, º6)

Write an equation of the line that passes through point P and is parallel tothe line with the given equation. (Lesson 3.6)

29. P(º4, º5), y = 6x º 7 30. P(2, º3), y = º!12!x + 4 31. P(º9, 8), x = º12

Decide whether lines p1 and p2 are perpendicular. (Lesson 3.7)

32. line p1: º7y + 3x = 6 33. line p1: 3y + 12x = 15 34. line p1: 16y º 2x = 11line p2: º9y º 21x = 3 line p2: 8y º 2x = 9 line p2: º12x º 2y = 6

Line j is perpendicular to the line with the given equation and line j passesthrough P. Write an equation of line j. (Lesson 3.7)

35. y = º2x + 1, P(4, º1) 36. 2x + 5y = 20, P(4, 10) 37. y = !12!x + 6, P(º2, º7)

70" 70"50"

130"

60"

60"

33"

A

C

F

B

35"

87"

E

D

86"

50"AF60"

DG

E

BC70"

20"

50"

30"

A

EC

D

B

y "

x "

62"

y "

110"

x "

y "

125" x "

y "

85"x "

y "

30"

x "y "

40"

x "



CHAPTER 4

In Exercises 1–4, the variable expressions represent the angle measures of atriangle. Find the measure of each angle. Then classify the triangle by itsangles. (Lesson 4.1)

1. m™E = x° 2. m™H = 60° 3. m™P = x° 4. m™S = (2x)°m™F = 3x° m™K = x° m™Q = (2x + 10)° m™T = (2x º 4)°m™G = 5x° m™L = x° m™R = (x + 10)° m™U = (2x º 2)°

5. The measure of an exterior angle of a right triangle is 135°. Find themeasures of the interior angles of the triangle. (Lesson 4.1)

Identify any figures that can be proved congruent. For those that can beproved congruent, write a congruence statement. (Lesson 4.2)

6. 7. 8.

9. Use the triangles in Exercise 6 above. Identify all pairs of congruentcorresponding angles and corresponding sides. (Lesson 4.2)

Use the given information to find the value of x. (Lesson 4.2)

10. ™Q £ ™T, ™R £ ™H 11. ™E £ ™K, ™F £ ™M 12. ™A £ ™C, ™BDA £ ™BDC

Decide whether enough information is given to prove that the triangles arecongruent. If there is enough information, state the congruence postulateyou would use. (Lesson 4.3)

13. ¤XVY, ¤ZVW 14. ¤MPN, ¤QPR 15. ¤BCE £ ¤DCE

16. Use the diagram in Exercise 13. Prove that ¤XYW £ ¤ZWY.

Is it possible to prove that the triangles are congruent? If so, state thecongruence postulate or theorem you would use. (Lesson 4.4)

17. 18. 19.

CD

E

Bq

P

M

R

N

Y

V

X

W

Z

D

B

C

52"(6x ! 2)"

AG

K

M

F

J

40"

28"

(8x ! 8)"

E

S

q

T

H

R

V

47"

70" 9x "

C

E

A

F D

BJ

L

G

M K

HC

H

D

FG

B EA

B

A C

E

D F

Extra Practice 809

8. none; corresponding sidesare congruent, but noinformation is given aboutthe corresponding angles.


Write a two-column proof or a paragraph proof. (Lesson 4.4)

20. GIVEN ! ADÆ ∞ BCÆ,ACÆ bisects BDÆ

PROVE ! ¤AED £ ¤CEB

State which postulate or theorem you can use to prove thatthe triangles are congruent. Then explain how proving that the triangles are congruent proves the given statement. (Lesson 4.5)

21. PROVE ! ABÆ £ CDÆ 22. PROVE ! ™GEF £ ™GHJ 23. PROVE ! ™RQT £ ™RST

Use the diagram and the information given below. (Lesson 4.5)

GIVEN ! ¤CBD £ ¤BAF¤BAF £ ¤FBD¤FBD £ ¤DFE

24. PROVE ! ™AFB £ ™BDF

25. PROVE ! BCÆ £ ABÆ

26. PROVE ! FDÆ £ DEÆ

Find the values of x and y. (Lesson 4.6)

27. 28. 29.

Place the figure in a coordinate plane. Label the vertices and give thecoordinates of each vertex. (Lesson 4.7)

30. A 4 unit by 3 unit rectangle with one vertex at (º5, 2)

31. A square with side length 6 and one vertex at (3, º4)

In the diagram, ¤EFG is a right triangle. Its base is 80 units and its height is 60 units. (Lesson 4.7)

32. Give the coordinates of points F and G.

33. Find the length of the hypotenuse of ¤EFG.

Place the figure in a coordinate plane and find the given information. (Lesson 4.7)

34. A rectangle with length 6 units and width 3 units; find the length of adiagonal of the rectangle.

35. An isosceles right triangle with legs of 7 units; find the length of the hypotenuse.

x "

y "

50"

x "y "

60" x "

y "

S

T

q

R

H

J

G

E

FBA

CD


A B

D C

E

B

A

C

E

D

F

G

F E (50, "20)

y

x


CHAPTER 5

Use the diagram shown. (Lesson 5.1)

1. In the diagram, DBÆ̆

fi ACÆ and BAÆ £ BCÆ. Find BC.


fi ACÆ and BAÆ £ BCÆ. Find DC.


is the perpendicular bisector of ACÆ. Because EA = EC = 13, what can you conclude about the point E?

Use the diagram shown. (Lesson 5.1)

4. In the diagram, m™FEH = m™GEH = 30°, m™HGE = m™HFE = 90°,and HF = 5. Find HG.

5. In the diagram, EHÆ̆

bisects ™JEM, m™EJK = m™EMK = 90° and JK = MK = 10. What can you conclude about point K?

In each case, find the indicated measure. (Lesson 5.2)

6. The perpendicular bisectors of 7. The perpendicular bisectors of ¤ABC meet at point D. Find AC. ¤EFG meet at point H. Find HJ.

8. The angle bisectors of ¤RST 9. The angle bisectors of ¤AECmeet at point Q. Find WS. meet at point G. Find GF.

Use the figure below and the given information. (Lesson 5.3)T is the centroid of ¤ABC, BT = 14, XC = 24, and TZ = 8.5.

10. Find the length of BYÆ.

11. Find the length of TXÆ.

12. Find the length of ATÆ.

Draw and label a large triangle of the given type and construct altitudes.Verify Theorem 5.8 by showing that the lines containing the altitudes areconcurrent and label the orthocenter. (Lesson 5.3)

13. an isosceles ¤MNP 14. an equilateral ¤DEF 15. a right isosceles ¤STR

F G

10

H

E

A C

26

J

W T

25Yq

S

R

7X

F

M15 K

E J G24

HF

G

E D

B

CA

10

6

Extra Practice 811

C

A

E DB13

13 1220

F

G

E

M

J

KH

A BX

C

Y ZT


Use ¤ABC, where X, Y, and Z are midpoints of the sides. (Lesson 5.4)

16. CBÆ ∞ !!!!!!?! . 17. XYÆ ∞ !!!!!!?! .

18. If AB = 8, then YZ = !!!!!!?! .

19. If AC = 10, then XY = !!!!!!?! .

20. If XZ = 6, then BC = !!!!!!?! .

21. If YZ = 4x º 11 and AB = 3x + 3, then YZ = !!!!!!?! .

22. If AZ = 4x º 5 and XY = 2x + 1, then AC = !!!!!!?! .

Name the shortest and longest sides of the triangle. (Lesson 5.5)

23. 24. 25.

Name the smallest and largest angles of the triangle. (Lesson 5.5)

26. 27. 28.

Complete with >, <, or =. (Lesson 5.6)

29. AC !!!? DF 30. QS !!!? TU 31. m™1 !!!? m™2

32. MN !!!? PR 33. m™1 !!!? m™2 34. m™1 !!!? m™2

35. JK !!!? ST 36. XY !!!? WV 37. m™1 !!!? m™2

2 1

14

10

9

860"

9

850"

X

YV

W

U

Z

K

J

T

S

L U

12

15 101

2

M

N120"

P

R110"q

L

1 2

S65"

U

q

R

TA

C

45"D

F

50"B E

6

S

5

7

R

T

11

P

5

10

N

q

12

M

8 10

K L

G

H

66"

47"

67"J

D E50" 35"

95"F

A C42"

86"

52"

B


C BY

Z X

A


CHAPTER 6

Decide whether the figure is a polygon. If it is, use the number of sides totell what kind of polygon the shape is. Then state whether the polygon isconvex or concave. (Lesson 6.1)

1. 2. 3.

4. 5. 6.

Use the information in the diagram to solve for x. (Lesson 6.1)

7. 8. 9.

Use the diagram of parallelogram VWXY at the right. Complete eachstatement, and give a reason for your answer. (Lesson 6.2)

10. VWÆ £ !!!!!!?! 11. ™VWX £ !!!!!!?!

12. XWÆ £ !!!!!!?! 13. VTÆ £ !!!!!!?!

14. ™XYW £ !!!!!!?! 15. WXÆ ∞ !!!!!!?!

16. ™VYX is supplementary to !!!!!!?! and !!!!!!?! .

17. Point T is the midpoint of !!!!!!?! and !!!!!!?! .

Are you given enough information to determine whether the quadrilateralis a parallelogram? Explain. (Lesson 6.3)

18. 19. 20.

Prove that the points represent the vertices of a parallelogram. (Lesson 6.3)

21. A(2, 4), B(4, º3), C(9, º6), D(7, 1) 22. E(º7, º1), F(º1, º2), G(º4, º9), H(º10, º8)

23. R(º5, 5), S(6, 4), T(2, º5), U(º9, º4) 24. M(º7, º3), N(6, 10), P(8, 4), Q(º5, º9)

70" 110"

J

N

K

M

(6x)"

102"

(7x # 13)"

(8x # 2)"(7x # 8)"

E

H

F

G

80"

115"

(5x ! 5)"

A

D

B

C

110"

70"

(3x # 5)"

(4x ! 10)"

Extra Practice 813

V

Y

W

X

T


List each quadrilateral for which the statement is true. (Lesson 6.4)

25. Adjacent angles are supplementary. 26. Adjacent angles are congruent.

27. Adjacent sides are perpendicular. 28. Diagonals are congruent.

29. Adjacent sides are congruent. 30. Opposite sides are parallel.

It is given that PQRS is a parallelogram. Graph ⁄PQRS. Decide whether itis a rectangle, a rhombus, a square, or none of the above. Justify youranswer using theorems about quadrilaterals. (Lesson 6.4)

31. P(6, 7), Q(º2, 1), R(6, º5), S(14, 1) 32. P(º6, 5), Q(4, 11), R(7, 7), S(º3, 1)

33. P(º2, 7), Q(4, 7), R(4, 1), S(º2, 1) 34. P(º7, º2), Q(º2, º2), R(º2, º7), S(º7, º7)

Find the missing angle measures. (Lesson 6.5)

35. 36. 37.

Find the value of x. (Lesson 6.5)

38. 39. 40.

What are the lengths of the sides of the kite? (Lesson 6.5)

41. 42. 43.

What kind of quadrilateral could EFGH be? EFGH is not drawn to scale. (Lesson 6.6)

44. 45. 46.

Find the area of the polygon. (Lesson 6.7)

47. 48. 49. 9

K

J

M 13

H

55

FE

G

10C

B

A

D8

1288

F

G

E

H

F

G

E

H

F

G

E

H

6K N

M

P

248

8

12E

F

H

G16 9

12

20

C

B

A

D15

1536

x

20

14

15

x

19

18

26

x

50"

G

F

E

H80"

65"R S

U T

10 10

110"B C

A D



CHAPTER 7

Use the graph of the transformation below. (Lesson 7.1)

1. Name the image of Q.

2. Name and describe the transformation.

3. Name two sides with the same length.

4. Name two angles with the same measure.

5. Name the coordinates of the preimage of point Y.

6. Show two corresponding sides have the same length,using the Distance Formula.

Name and describe the transformation. Then name the coordinates of thevertices of the image. (Lesson 7.1)

7. 8.

Use the diagrams to complete the statement. (Lesson 7.1)

9. ¤CBA ˘ !!!!!!?! 10. ¤DEF ˘ !!!!!!?! 11. !!!!!!?! ˘ ¤KNM

Use the diagram at the right to name the image of¤ABC after the reflection. If the reflection does notappear in the diagram, write not shown. (Lesson 7.2)

12. Reflection in the x-axis

13. Reflection in the y-axis

14. Reflection in the line y = x

15. Reflection in the x-axis, followed by a reflection in the y-axis

Find the coordinates of the reflection without using a coordinate plane. Thencheck your answer by plotting the image and preimage on a coordinate plane.(Lesson 7.2)

16. M(5, 2) reflected in the x-axis 17. N(º2, 4) reflected in the y-axis

18. P(1, º8) reflected in the y-axis 19. Q(1, 12) reflected in the x-axis

K M

N

560!

J

H

G

3

30!100!F

E

D

560!

A

B

C

3

30! 100!

y

x3

1

J

K

L

M

N

PR

œ

y

x1

1A

B C

D E

F G

H

Extra Practice 815

y

x1

4

P

R

œ

Z

Y

X

y

x1

1

B C E F

GAN

M P

H

K J


Find point C on the x-axis so AC + BC is a minimum. (Lesson 7.2)

20. A(1, 2), B(12, 5) 21. A(3, 7), B(11, 7) 22. A(º2, 7), B(º9, 5)

Name the coordinates of the vertices of the image after a clockwiserotation of the given number of degrees about the origin. (Lesson 7.3)

23. 90° 24. 270° 25. 180°

In the diagram, a ∞ b, ¤JKM is reflected in line a and¤J’K’M’ is reflected in line b. (Lesson 7.4)

26. A translation of ¤JKM maps onto which triangle?

27. Which lines are perpendicular to KKfl¯˘

?

28. Name two segments parallel to MMfl¯˘

.

Copy figure RSTV and draw its image after the translation. Then describethe translation using a vector in component form. (Lesson 7.4)

29. (x, y) ˘ (x º 3, y + 5)

30. (x, y) ˘ (x + 1, y º 4)

31. (x, y) ˘ (x º 7, y + 7)

32. (x, y) ˘ (x + 2, y º 6)

Sketch the image of A(º6, º2) after the described glide reflection. (Lesson 7.5)

33. Translation: (x, y) ˘ (x + 1, y + 3) 34. Translation: (x, y) ˘ (x + 4, y º 3)Reflection: in the x-axis Reflection: in x = º4

Sketch the image of ¤GHK after a composition using the giventransformations in the order they appear. (Lesson 7.5)

35. G(5, 3), H(º2, 6), K(º1, º4) 36. G(2, 1), H(0,º6), K(º5, º4)

Translation: (x, y) → (x º 7, y) Translation: (x, y) → (x + 8, y)Reflection: in the x-axis Reflection: in the x-axis

Describe each frieze pattern according to the following seven categories: T, TR, TG, TV, THG, TRVG, and TRHVG. (Lesson 7.6)

37. 38.

y

x

4

N

M

K

J

O!1

y

x

1

3

B

CA

O

y

x

3

1

E F

GHO


a bK

J

M

K ’

J ’

M ’

K ’’

J ’’

M ’’

R

S T

y

x1

1

V


CHAPTER 8

Rewrite the fraction so that the numerator and denominator have thesame units. Then simplify. (Lesson 8.1)

1. "2550mcm" 2. "

145yfdt

" 3. "125

fint.

" 4. "19000

kmm"

Use ratios to solve the following problems. (Lesson 8.1)

5. The measures of the angles in a quadrilateral are in the extended ratio of 3:4:5:6. Find the measures of the angles.

6. The perimeter of isosceles triangle ABC is 35 cm. The extended ratio of AB :BC :AC is x :3x :3x. Find the lengths of the three sides.

Solve the proportion. (Lesson 8.1)

7. "2a1" = "

13" 8. "

ºb5" = "

280" 9. "

º62" = "º

c9"

10. "d +7

5" = "288" 11. "º

29" = "

f º9

3" 12. "

111" = "gg

+º

64"

Complete the sentence. (Lesson 8.2)

13. If "1x0" = "

3y0" , then "3

x0" = "

??". 14. If "

94" = "

xy", then "

143" = "

??".

15. If "9x" = "

1y2" , then "

34" = "

??". 16. If "1

z2" = "8

y", then "z +

1212

" = "??".

Find the geometric mean of the two numbers. (Lesson 8.2)

17. 4 and 9 18. 1 and 4 19. 2.5 and 10

20. 9 and 16 21. 256 and 4 22. 100 and 10,000

Use the diagram and the given information to find the unknown length.(Lesson 8.2)

23. GIVEN ! "PSR

S" = "T

PQT", find SR. 24. GIVEN ! "E

CGE" = "DFH

F", find CE.

In the diagram, PQRS ~ TVWX. (Lesson 8.3)

25. Find the scale factor of PQRS to TVWX.

26. Find the scale factor of TVWX to PQRS.

27. Find the values of u, y, and z.

28. Find the perimeter of each polygon.

Extra Practice 817

P

R

S

q

T5 8

10

C E G

H

D

F9

12

10

S

P

6

15 R

9 q

u WzX

y

T 6 V

6


Determine whether the triangles can be proved similar. If they are similar,write a similarity statement. If they are not similar, explain why. (Lesson 8.4)

29. 30. 31.

Find coordinates for point Z so that ¤OWX ~ ¤OYZ. (Lesson 8.4)

32. O(0, 0), W(4, 0), X(0, 3), Y(12, 0) 33. O(0, 0), W(2, 0), X(0, 5), Y(5, 0)

34. O(0, 0), W(º4, 0), X(0, 2), Y(º6, 0) 35. O(0, 0), W(º1, 0), X(0, º4), Y(º3, 0)

Are the triangles similar? If so, state the similarity and the postulate ortheorem that justifies your answer. (Lesson 8.5)

36. 37. 38.

Determine whether the triangles are similar. If they are, write a similaritystatement and solve for the variable. (Lesson 8.5)

39. 40. 41.

Determine whether the given information implies that QSÆ

∞ PTÆ

. Explain.(Lesson 8.6)

42. 43.

Find the value of the variable. (Lesson 8.6)

44. 45.

Use the origin as the center of the dilation and the given scale factor to findthe coordinates of the vertices of the image of the polygon. (Lesson 8.7)

46. A (º2, 3), B(º1, 5), C(3, 3), D(2, º4), k = 2 47. A(2, 0), B(5, 3), C(4, 5), D(1, 3), k = 5

48. A(3, º6), B(6, º6), C(6, 9), D(º3, 9), k = "13" 49. A(4, º4), B(6, 4), C(2, 8), D(º8, º4), k = "

14"

24

x5

6A C B

D

4 3

6x

P T

S

Uq

8

4 1

2

T

P q

S

V8 20

18

7

H K

J

x12

16

F

E G

3

42

q

5

15

7

20

21M R

P

N

x

C

B

A E

6 x

D6

15

918

P q

S T

R14

7

14

7

G

10

J

H24

MK 8

N6

D F

E

6

12

15A C

B52

4

K

M

G

H

J65!

45!

70!

E

D F

B

A C50!

40!

R

Sq

U T

V45!

30!

45!



CHAPTER 9

Write similarity statements for the three similar triangles in the diagram.Then complete the proportion. (Lesson 9.1)

1. "AA

DC" = "A

?B" 2. "E

?H" = "G

EHH" 3. "

JKMJ" = "

K?J"

Find the value of the variable. (Lesson 9.1)

4. 5. 6.

Find the unknown side length. Simplify answers that are radicals. Tellwhether the side lengths form a Pythagorean triple. (Lesson 9.2)

7. 8. 9.

The variables r and s represent the lengths of the legs of a right triangle,and t represents the length of the hypotenuse. The values of r, s, and tform a Pythagorean Triple. Find the unknown value. (Lesson 9.2)

10. r = 7, t = 25 11. r = 5, s = 12 12. s = 25, t = 65

13. r = 49, s = 168 14. s = 198, t = 202 15. r = 21, t = 35

Find the area of the figure. Round decimal answers to the nearest tenth.(Lesson 9.2)

16. 17. 18.

Tell whether the triangle is a right triangle. (Lesson 9.3)

19. 20. 21. X

Z

12

Y21

3!65

RP

12

q

14

19

7 TS

5

U

2!6

9 cm

KH L

9 cmJ

14 cm

16 cm

GD F

12 cm

E

8 cm6 cm

C

A B8 cm

14

V48

U

TS

q

26

R

10

N

M

6

5

P

A

B20

60 x

C

D

S T U2

4

V

xN

q PR

18

12x

E

FG H

J

L

K

M

A

BC

D

Extra Practice 819


Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. (Lesson 9.3)

22. 17, 18, 19 23. 15, 36, 39 24. 3, 5, 8

25. 7, 9, 12 26. 100, 300, 500 27. !9"1", 12, 20

Find the value of each variable. Write answers in simplest radical form.(Lesson 9.4)

28. 29. 30.

Find the sine, the cosine, and the tangent of the acute angles of thetriangle. Express each value as a decimal rounded to four places. (Lesson 9.5)

31. 32. 33.

Find the value of each variable. Round decimals to the nearest tenth.(Lesson 9.5)

34. 35. 36.

Solve the right triangle. Round decimals to the nearest tenth. (Lesson 9.6)

37. 38. 39.

Draw vector PQÆ„

in a coordinate plane. Write the component form of thevector and find its magnitude. Round your answer to the nearest tenth.(Lesson 9.7)

40. P(2, 3), Q(5, 7) 41. P(º1, º5), Q(3, 6) 42. P(º4, 3), Q(2, º8)

Let a„

= #3, 5$, b„= #º7, 2$, c„ = #1, º6$, and d„

= #2, 9$. Find the given sum.(Lesson 9.7)

43. a„ + b„ 44. a„ + c„ 45. c„ + d„ 46. b„ + c„

M221N

P

140

E

D10

5

FBC 12

15

A

G

w

H

17

38!z J

F

y

E 8

65! x

D

A

C

u

B 1542!

v

Z

Y

20

X 29

21

W

U

4

V

5

!41

R

S

33

T

65

56

Gy

H

20 x

J

60!

E y D

8 x

F

30!

B

y C

7 x

A45!



CHAPTER 10

Match the notation with the term that best describes it. (Lesson 10.1)

1. EFÆA. Secant

2. G B. Chord

3. HJ¯̆

C. Radius

4. BFÆD. Diameter

5. A E. Point of tangency

6. KF¯̆

F. Common external tangent

7. CD¯̆

G. Common internal tangent

8. GKÆH. Center

Tell whether the common tangent(s) are internal or external. (Lesson 10.1)

9. 10. 11.

Use the diagram at the right. (Lesson 10.1)

12. What are the center and radius of ›C?

13. What are the center and radius of ›D?

14. Describe the intersection of the two circles.

15. Describe all the common tangents of the two circles.

ADÆ

and BEÆ

are diameters. Copy the diagram. Find the indicated measure.(Lesson 10.2)

16. mAB! 17. mDC!18. mAC! 19. mED!20. m™CQE 21. m™AQE

22. mBC! 23. mBDC"

Find the value of each variable. (Lesson 10.3)

24. 25. 26.

40!

x !y !70!

x !

130! x !

Extra Practice 821

AC

E

G B

H

J

D

K F

1

y

1 xC D

AD

B

E

C

q

55!

35!



27. 28. 29.

30. 31. 32.


33. 34. 35.

36. 37. 38.

Give the center and radius of the circle. (Lesson 10.6)

39. (x º 12)2 + (y + 3)2 = 49 40. (x + 15)2 + y2 = 20

41. (x + 3.8)2 + (y º 4.9)2 = 0.81 42. (x º 1)2 + (y + 7)2 = 1

Write the standard equation of the circle with the given center and radius.(Lesson 10.6)

43. center (5, 8), radius 6 44. center (–2, 7), radius 10

Use the given information to write the standard equation of the circle.(Lesson 10.6)

45. The center is (2, 2); a point on the circle is (2, 0).

46. The center is (0, 1); a point on the circle is (º3, 1).

Use the graph at the right to write equation(s) for the locus of points in thecoordinate plane that satisfy the given condition. (Lesson 10.7)

47. equidistant from A and B 48. 5 units from A

49. 4 units from AB¯̆

50. 6 units from B

45

x8

12x

45

36

x " 5

x

45

36x

8

3

9

x3x

23

6

x

x !88!

180!x !

110!

x !

125!

45!

x !85! 75!

x !

120!

x !


1

y

1

x

A B


CHAPTER 11

Find the sum of the measures of the interior angles of the convex polygon.(Lesson 11.1)

1. 36-gon 2. 45-gon 3. 60-gon 4. 90-gon


5. 6. 7.

You are given the number of sides of a regular polygon. Find the measureof each exterior angle. (Lesson 11.1)

8. 180 9. 24 10. 48 11. 36

You are given the measure of each exterior angle of a regular n-gon. Findthe value of n. (Lesson 11.1)

12. 40° 13. 18° 14. 45° 15. 90°

Find the measure of a central angle of a regular polygon with the givennumber of sides. (Lesson 11.2)

16. 10 sides 17. 18 sides 18. 25 sides 19. 90 sides

Find the perimeter and area of the regular polygon. (Lesson 11.2)

20. 21. 22.

23. 24. 25.

In Exercises 26–28, the polygons are similar. Find the ratio (red to blue) oftheir perimeters and of their areas. (Lesson 11.3)

26. 27. 28.

29. The ratio of the perimeters of two similar hexagons is 5:8. The area of thelarger hexagon is 320 square inches. What is the area of the smaller hexagon?(Lesson 11.3)

96

31

146

5

8

7

1036

x !140!

x !100!145!

130!

140!150!130!

x !

Extra Practice 823


Find the indicated measure. (Lesson 11.4)

30. Circumference 31. Radius

Find the indicated measure. (Lesson 11.4)

32. Length of MN! 33. Circumference 34. Radius

35. Length of AB! 36. Circumference 37. Radius

Find the area of the shaded region. (Lesson 11.5)

38. 39. 40.

41. 42. 43.

Find the probability that a point K, selected randonly on MNÆ

, is on thegiven segment. (Lesson 11.6)

44. ABÆ45. ADÆ 46. MAÆ

47. MDÆ

Find the probability that a randomly chosen point in the figure lies in the shaded region. (Lesson 11.6)

48. 49.6

B5

A

C D

E

S170!R T

10C 75!

B

8D

S

q

2252!

R

Pq12

4

D

F

E110!

75N

MK 45!70!15

E

F

D135!

5A B

C

65!5

V

U

T120! 49

S

R

q60!9

M

NA

r C § 57 ftr

r # 12 in.


110 1 2 3 4 5 6 7 8 9 10

M

12

A B C D N


CHAPTER 12

Tell whether the solid is a polyhedron. If it is, decide whether it is regularand/or convex. Explain. (Lesson 12.1)

1. 2. 3.

Count the number of faces, vertices, and edges of the polyhedron. Verifyyour results using Euler’s Theorem. (Lesson 12.1)

4. 5. 6.

Describe the cross section. (Lesson 12.1)

7. 8.

Find the surface area of the right prism. (Lesson 12.2)

9. 10. 11.

Find the surface area of the right cylinder. Round the result to two decimalplaces. (Lesson 12.2)

12. 13. 14.

Find the surface area of the solid. The pyramids are regular and the cone isright. (Lesson 12.3)

15. 16. 17.

12 cm

5 cm

Area # 93.5 cm2

6 cm

8 cm

5 in.

6 in.

6 in.15 cm

6 cm5 in.

5 in.

12 in.

5 in.2 in.3 cm

8 cm4 cm

5 cm10 cm

Extra Practice 825



Find the volume of the solid. (Lesson 12.4)

18. Right rectangular prism 19. Right cylinder 20. Oblique square prism

21. Oblique cylinder 22. Two holes are drilled 23. A square “hole” is cutthrough a cube. from a cylinder.

Find the volume of the pyramid or cone. (Lesson 12.5)

24. 25. 26.

27. 28. 29.

Find the surface area and the volume of the sphere. Round your result totwo decimal places. (Lesson 12.6)

30. 31. 32.

The solid is similar to a larger solid with the given scale factor. Find thesurface area S and volume V of the larger solid. (Lesson 12.7)

33. Scale factor 2:3 34. Scale factor 3:5 35. Scale factor 5:7

S = 100π cm2

V = 166"23"π cm3

S = 104π ft2

V = 144π ft3S = 96 m2

V = 64 m3

36 in.13 m

8 cm

13 ft

8 ft

7.5 mm

15 mm7 in.

10 in.

9 in.

6 in.15 cm

18 cm

10 cm

12 cm

3 ft

4 ft6 ft

2 cm

5 cm

5 cm5 cm

13 in.

7 in.

13 cm

20 cm6 ft

15 ft

18 in.

11 in.

10 in.

1980 in.3 about 1060.29 ft33380 cm3

about 2001.19 in.3

about 93.58 cm3about 247.59 ft3

480 cm3 701.48 cm3 162 in.3

about 513.13 in.3 about 883.57 mm3 about 871.27 ft3

804.25 cm2; 2144.66 cm3 2123.72 m2; 9202.77 m3 4701.50 in.2; 24,429.02 in.3

196π cm2; 457}13}π cm3about 288.89π ft2; about 666.67π ft3;

216 m2; 216 m3


Extra Practice - Mrs. Sevilla's Math...

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