E actic Pr - crunchy math

[Pages:7]Glencoe Geometry

A3

Chapter 7

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1 Skills Practice

Proportions

1. FOOTBALL A tight end scored 6 touchdowns in 14 games. Find the ratio of touchdowns per game. 0.43:1

2. EDUCATION In a schedule of 6 classes, Marta has 2 elective classes. What is the ratio of elective to non-elective classes in Marta's schedule?

1:2

3. BIOLOGY Out of 274 listed species of birds in the United States, 78 species made the endangered list. Find the ratio of endangered species of birds to listed species in the United States. 13397

4. ART An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog. 21 in.

5. SCHOOL The ratio of male students to female students in the drama club at Campbell High School is 3:4. If the number of male students in the club is 18, what is the number of female students? 24

Solve each proportion.

6. 25 4x0 16

9. 54x 385 3.5

7. 170 2x1 30 10. x 31 72 9.5

8. 250 46x 6 11. 135 x 53 28

Find the measures of the sides of each triangle. 12. The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is

450 centimeters.

90 cm, 150 cm, 210 cm

13. The ratio of the measures of the sides of a triangle is 5:6:9, and its perimeter is 220 meters.

55 m, 66 m, 99 m

14. The ratio of the measures of the sides of a triangle is 4:6:8, and its perimeter is 126 feet.

28 ft, 42 ft, 56 ft

15. The ratio of the measures of the sides of a triangle is 5:7:8, and its perimeter is 40 inches.

10 in., 14 in., 16 in.

Chapter 7

8

Glencoe Geometry

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 7-1

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1 Practice

Proportions

1. NUTRITION One ounce of cheddar cheese contains 9 grams of fat. Six of the grams of fat are saturated fats. Find the ratio of saturated fats to total fat in an ounce of cheese. 2:3

2. FARMING The ratio of goats to sheep at a university research farm is 4:7. The number of sheep at the farm is 28. What is the number of goats? 16

3. ART Edward Hopper's oil on canvas painting Nighthawks has a length of 60 inches and a width of 30 inches. A print of the original has a length of 2.5 inches. What is the width of the print? 1.25 in.

Solve each proportion.

4. 58 1x2 7.5

7. x 32 89 23

5. 1.x12 15 0.224 8. 3x 45 75 57

6. 267x 43 6 9. x 42 x 24 10

Find the measures of the sides of each triangle.

10. The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet.

24 ft, 32 ft, 48 ft

11. The ratio of the measures of the sides of a triangle is 7:9:12, and its perimeter is 84 inches.

21 in., 27 in., 36 in.

12. The ratio of the measures of the sides of a triangle is 6:7:9, and its perimeter is 77 centimeters.

21 cm, 24.5 cm, 31.5 cm

Find the measures of the angles in each triangle.

13. The ratio of the measures of the angles is 4:5:6.

48, 60, 72

14. The ratio of the measures of the angles is 5:7:8.

45, 63, 72

15. BRIDGES The span of the Benjamin Franklin suspension bridge in Philadelphia, Pennsylvania, is 1750 feet. A model of the bridge has a span of 42 inches. What is the ratio of the span of the model to the span of the actual Benjamin Franklin Bridge? 5100

Chapter 7

9

Glencoe Geometry

Answers

Answers (Lesson 7?1)

Glencoe Geometry

A7

Chapter 7

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2 Skills Practice

Similar Polygons

Determine whether each pair of figures is similar. Justify your answer.

1.

B

E

6

9

4

6

A 59

35 10.5

D C

59

35 7

F

2.

P3 Q

3

3

S 3R

W 7.5

Z 7.5

7.5 X 7.5

Y

ABC DEF; A D, C F, and B E because if two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent;

ADBE BECF CFDA 32.

rhombus PQRS rhombus WXYZ; P W, Q X, R Y, S Z; WPQX QXYR RYSZ ZSWP 73.5 0.4

Each pair of polygons is similar. Write a similarity statement, and find x, the measure(s) of the indicated side(s), and the scale factor.

3. GH

A 12

B

14 D

E7H

13 6

x

F 13 G

26

C

ABCD EFGH; 612; 612; 2

4. ST and SU

W

T x 5

4 4S

9

Y 3X

x 5

U

WXY STU (or SUT ) 7; 12; 12; 13

5. WT

S

T x1 W

P

9

5

U 10 V

Q

R

3

PQRS UVWT; 5; 6; 32

6. TS and SP

M 10 N

8

L

P

x 2

T x 1 S

LMN TSP; 13; 12; 15; 23

Chapter 7

16

Glencoe Geometry

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 7-2

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2 Practice

Similar Polygons

Determine whether each pair of figures is similar. Justify your answer.

1.

L 15 K

24

20

M

25

J

P 14.4

15

S 9

Q 12 R

2. B

14

16

C 12 A

T

18

21

U

24

V

JKLM QRSP ; J Q, K R, L S, M P, and QJKR RKSL LSMP PMQJ 53 or 1.67

ABC UVT; A U, B V, and C T by the Third Angle Theorem and UABV BVCT CTUA 23.

Each pair of polygons is similar. Write a similarity statement, and find x, the measure(s) of the indicated side(s), and the scale factor.

3. LM and MN

D

C

10

A

14 B

N x6 M x 9

P

L

4. DE and DF

A 6 B 40

12 F

x 1 C

E 40 x 3 D

ABCD LMNP ; 32; 10 12; 712; 43

ABC DEF; 7; 4; 8; 32

5. COORDINATE GEOMETRY Triangle ABC has vertices A(0, 0), B(4, 0), and C(2, 4). The coordinates of each vertex are multiplied by 3 to create AEF. Show that AEF is similar to ABC.

AB 4, BC CA 25 and AE 12, EF FA 65. AABE BECF CFAA 13; A A and since BC || EF, B E and C F. Since the corresponding angles are congruent and the corresponding sides are proportional, ABC AEF.

6. INTERIOR DESIGN Graham used the scale drawing of his living room to decide where to place furniture. Find the dimensions of the living room if the scale in the drawing is 1 inch 4.5 feet.

18 ft by 11 ft 3 in.

21?2 in. 4 in.

Chapter 7

17

Glencoe Geometry

Answers

Answers (Lesson 7?2)

Glencoe Geometry

A10

Chapter 7

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3 Study Guide and Intervention (continued)

Similar Triangles

Use Similar Triangles Similar triangles can be used to find measurements.

Example 1 ABC DEF. Find x and y.

y

B

E

18

18 9

A

183

C D xF

DACF BECF

18x3 198

18x 9(183)

DABE BECF

y 18

198

9y 324

x 93

y 36

Example 2 A person 6 feet tall casts a 1.5-foot-long shadow at the same time that a flagpole casts a 7-foot-long shadow. How tall is the flagpole?

? 6 ft

1.5 ft

7 ft

The sun's rays form similar triangles. Using x for the height of the pole, 6x 17.5 , so 1.5x 42 and x 28. The flagpole is 28 feet tall.

Exercises

Each pair of triangles is similar. Find x and y.

1.

y 10

35

20

13 x

2. x 2

20 y 26

13

x 26; y 17.5

x 24; y 30

3.

362

x

y

36

24 36

x 12; y 242

4.

38.6

23

60

30 x y

x 19.3; y 46

5.

9

y

7.2

x

8

16

x 18; y 10.8

6.

10

30

22

y

32

x

x 1023; y 1612

7. The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter post casts a shadow that is 0.85 meter long, what is the length of the longer post's shadow

to the nearest hundredth? 3.78 m

Chapter 7

22

Glencoe Geometry

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 7-3

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3 Skills Practice

Similar Triangles

Determine whether each pair of triangles is similar. Justify your answer.

1.

T

13

9

R 14 S W

Y

21

12

20

X

2. B

8

12

A

12

R

9Q

9

6

C

P

No; the sides are not proportional. yes; ABC PQR (or QPR ); SSS Similarity

3.

P

T

U 15

10 70 14 S

J

70 21

M

yes; STU JPM; SAS Similarity

4.

M

T

S

60 K

Q

30

R

yes; SKM RTQ; AA Similarity

ALGEBRA Identify the similar triangles, and find x and the measures of the indicated sides.

5. AC and ED

A x1 E 15 B 12 C

x 5 D

6. JL and LM

J x 18

16

K

LN x3 M4

ABC DBE; 15; 16; 20

JKL MNL; 10; 28; 7

7. EH and EF

H9 F

E

6

12

x5 G 9D

DEF GEH; 4; 9; 18

8. VT and ST

S x 4

14

V

6 x6

R

UT

RST UVT; 7.5; 1.5; 5

Chapter 7

23

Glencoe Geometry

Answers (Lesson 7?3)

Glencoe Geometry

A11

Chapter 7

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3 Practice

Similar Triangles

Determine whether each pair of triangles is similar. Justify your answer.

1.

J

18

A 42

24

Y

16 42

S

12

KW

yes; JAK WSY; SAS Similarity

2.

L

M

S

16

12.5 11

18

NT

14

R

16

No; the sides are not proportional.

ALGEBRA Identify the similar triangles, and find x and the measures of the indicated sides.

3. LM and QP

L x 3

18 N

Q x 1

12 P

M

LMN PQN; 9; 12; 8

4. NL and ML

N x5 M 6x 2

J 8K

L

24

JLN KLM; 2; 21; 14

Use the given information to find each measure.

5. If TS || QR, TS 6, PS x 7,

QR 8, and SR x 1, find PS and PR.

Q T

P

S

R

6. If EF || HI, EF 3, EG x 1,

HI 4, and HG x 3, find EG and HG.

I

G

H

E

F

PS 12; PR 16

EG 6; HG 8

INDIRECT MEASUREMENT For Exercises 7 and 8, use the following information. A lighthouse casts a 128-foot shadow. A nearby lamppost that measures 5 feet 3 inches casts an 8-foot shadow.

7. Write a proportion that can be used to determine the height of the lighthouse.

Sample answer: If x height of lighthouse, 5.x25 1288 .

8. What is the height of the lighthouse? 84 ft

Chapter 7

24

Glencoe Geometry

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 7-3

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3 Word Problem Practice

Similar Triangles

1. MINIATURES Marla likes her chair so much that she decides to make a miniature replica of it for her pet hamster. Find the value of x.

15"

4. SHADOWS A radio tower casts a shadow 8 feet long at the same time that a vertical yardstick casts a shadow half an inch long. How tall is the radio tower?

576 ft

14"

x 3.5"

3.75 in.

2. MODELS Jim has a scale model of his sailboat. The figure shows drawings of the original sailboat and the model. Find x.

203 in.

x in.

MOUNTAIN PEAKS For Exercises 5 and 6, use the following information.

Gavin and Brianna want to know how far a mountain peak is from their houses. They measure the angles between the line of site to the peak and to each other's houses and carefully make the drawing shown.

Gavin

2 in.

0.246 in. 90?

Peak

83?

2.015 in.

Brianna

The actual distance between Gavin and

52?

Brianna's house is 112 miles.

10.15 in. 8 in.

5. What is the actual distance of the

52?

160 in.

mountain peak from Gavin's house? Round your answer to the nearest

3. GEOMETRY Georgia draws a regular pentagon and starts connecting its

tenth of a mile.

12.2 mi

vertices to make a

A

5-pointed star. After

drawing three of the

lines in the star, she D

becomes curious

E

about two triangles

that appear in the

figure, ABC and

B

C

6. What is the actual distance of the mountain peak from Brianna's house? Round your answer to the nearest tenth of a mile.

12.3 mi

BCE. They look similar to her. Prove

that this is the case.

Sample answer: mADB 108, so mDBA 36 (base of isosceles ABD). Thus, mABC 72?. Similarly, mDCB 36? and mACB 72?. So, mBEC 72? and mBAC 36?. Therefore, ABC and BCE are similar.

Chapter 7

25

Glencoe Geometry

Answers

Answers (Lesson 7?3)

Glencoe Geometry

A14

Chapter 7

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4 Skills Practice

Parallel Lines and Proportional Parts

1. If JK 7, KH 21, and JL 6, find LI.

KJ

H

L

I

18

2. Find x and TV if RU 8, US 14, TV x 1 and VS 17.5.

S

U R

11; 10

V T

Determine whether BC || DE.

3. AD 15, DB 12, AE 10, and EC 8

yes

4. BD 9, BA 27, and CE is one third of EA

no

5. AE 30, AC 45, and AD is twice DB

yes

DB

A

EC

COORDINATE GEOMETRY For Exercises 6?8, use the following information.

Triangle ABC has vertices A(5, 2), B(1, 8), and C(4, 2). Point D is the midpoint of AB and E is the midpoint of AC.

yB D

6. Identify the coordinates of D and E.

D(2, 5); E(0.5, 2)

A

E

C

O

x

7. Show that BC is parallel to DE.

Since the slope of BC is 2 and the slope of DE is 2, BC is parallel to DE.

8.

Show that DE 12BC.

The length of DE is

1 1.25

or

245

or

325

and

the

length

of

BC

is

45

or 35.

9. Find x and y.

10. Find x and y.

2x 1 x 7

3y 8 y 5

2y 1

x 3

3y 5

3?2x 2

x 6, y 6.5

x 2, y 4

Chapter 7

30

Glencoe Geometry

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 7-4

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4 Practice

Parallel Lines and Proportional Parts

1. If AD 24, DB 27, and EB 18, find CE.

C

E

AD

B

16

2. Find x, QT, and TR if QT x 6, SR 12, PS 27, and TR x 4.

P

SR

T

Q

12; 18; 8

Determine whether JK || NM.

3. JN 18, JL 30, KM 21, and ML 35

no

4. KM 24, KL 44, and NL 56JN

yes

K M

JN

L

COORDINATE GEOMETRY For Exercises 5 and 6, use the following information. Triangle EFG has vertices E(4, 1), F(2, 5), and G(2, 1). Point K is the midpoint of EG and H is the midpoint of FG.

5. Show that EF is parallel to KH.

The slope of EF is 1 and the slope of KH is 1, so EF is parallel to KH.

6. Show that KH 12EF.

The length of KH is 32, and the length of EF is 62.

yF

H

O

x

E

K

G

7. Find x and y.

3x 4 5?4x 3

2?3y 3 1?3y 6

x 4, y 9

8. Find x and y.

4?3y 2 4y 4

3x 4 x 1

x 52, y 94

9. MAPS The distance from Wilmington to Ash Grove along Kendall is 820 feet and along Magnolia, 660 feet. If the distance between Beech and Ash Grove along Magnolia is 280 feet, what is the distance between the two streets along Kendall?

about 348 ft

Chapter 7

31

Magnolia

Wilmington

Beech Ash Grove

Kendall

Glencoe Geometry

Answers (Lesson 7?4)

Glencoe Geometry

A17

Chapter 7

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5 Study Guide and Intervention (continued)

Parts of Similar Triangles

Special Segments of Similar Triangles When two triangles are similar,

corresponding altitudes, angle bisectors, and medians are proportional to the corresponding sides. Also, in any triangle an angle bisector separates the opposite side into segments that have the same ratio as the other two sides of the triangle.

Example 1 In the figure, ABC XYZ, with angle bisectors as shown. Find x.

B

Y

24 10

x 8

X

WZ

A

D

C

Since ABC XYZ, the measures of the angle bisectors are proportional to the measures of a pair of corresponding sides. AXBY YBWD 2x4 180 10x 24(8)

10x 192

x 19.2

Example 2 SU bisects RST. Find x.

S

15

30

R x U 20 T

Since SU is an angle bisector, RTUU RTSS . 2x0 1350 30x 20(15) 30x 300

x 10

Exercises

Find x for each pair of similar triangles.

1.

x

20

18

36

2.

12

9

x6

10

8

3.

4

3

2.25

3x

4.

x 10

10

8.75

78 8

5.

11

x

17

x 7

1256

6.

x 1

16

28

2x 2

15

Chapter 7

36

Glencoe Geometry

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 7-5

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5 Skills Practice

Parts of Similar Triangles

Find the perimeter of the given triangle.

1. JKL, if JKL RST, RS 14, ST 12, TR 10, and LJ 14

T

L

R

S

J

K

2. DEF, if DEF ABC, AB 27, BC 16, CA 25, and FD 15

C

A

F

D

B

E

50.4

40.8

3. PQR, if PQR LMN, LM 16, MN 14, NL 27, and RP 18

N R

P

Q

L

M

38

4. KLM, if KLM FGH, FG 30, GH 38, HF 38, and KL 24

G L HM

K F

84.8

Use the given information to find each measure.

5. Find FG if RST EFG, SH is an altitude of RST, FJ is an altitude of EFG, ST 6, SH 5, and FJ 7.

F S

6. Find MN if ABC MNP, AD is an altitude of ABC, MQ is an altitude of MNP, AB 24, AD 14, and MQ 10.5.

A M

R

H TE

8.4

JG

DC

18

BQP

N

Find x.

7. HKL XYZ

K Y

10

H

18

813

x

LX

15

8.

24

20

Z

8.4

x 7

Chapter 7

37

Glencoe Geometry

Answers

Answers (Lesson 7?5)

Glencoe Geometry

A18

Chapter 7

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5 Practice

Parts of Similar Triangles

Find the perimeter of the given triangle.

1. DEF, if ABC DEF, AB 36, BC 20, CA 40, and DE 35

B E

2. STU, if STU KLM, KL 12, LM 31, MK 32, and US 28

MU TL

AD

FC

93.3

S K

65.625

Use the given information to find each measure.

3. Find PR if JKL NPR, KM is an altitude of JKL, PT is an altitude of NPR, KL 28, KM 18, and

PT 15.75.

K

P

4. Find ZY if STU XYZ, UA is an altitude of STU, ZB is an altitude of XYZ, UT 8.5, UA 6, and ZB 11.4.

Z

U

JM

24.5

LN T

R

S T AX

16.15

Y

B

Find x. 5.

2x 1

13.5

40

x 4

25

6.

20

30

x 28

16.8

PHOTOGRAPHY For Exercises 7 and 8, use the following information. Francine has a camera in which the distance from the lens to the film is 24 millimeters.

7. If Francine takes a full-length photograph of her friend from a distance of 3 meters and the height of her friend is 140 centimeters, what will be the height of the image on the

film? (Hint: Convert to the same unit of measure.) 11.2 mm

8. Suppose the height of the image on the film of her friend is 15 millimeters. If Francine took a full-length shot, what was the distance between the camera and her friend?

2.24 m

Chapter 7

38

Glencoe Geometry

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5 Word Problem Practice

Parts of Similar Triangles

1. JOGGING Macy wants to jog around Triangle Park. On a scale map, the park has a perimeter of 11 inches. The scale of the map is 1 inch : 100 yards. What is the perimeter of the actual park?

1100 yd

4. FLAG POLES A flag pole attached to the side of a building is supported with a network of strings as shown in the figure.

F D

2. TENTS Jana went camping and stayed in a tent shaped like a triangle. In a photo of the tent, the base of the tent is 6 inches and the altitude is 5 inches. The actual base was 12 feet long. What was the height of the actual tent?

E C

AB

The rigging is done so that AE EF, AC CD, and AB BC. What is the ratio of CF to BE?

2 :1

x

10 ft

3. PLAYGROUND The playground at Hank's school has a large right triangle painted in the ground. Hank starts at the right angle corner and walks toward the opposite side along an angle bisector and stops when he gets to the hypotenuse.

A

50 ft 30 ft

45?

40 ft

B

How much farther from Hank is point B versus point A?

717 ft

COPIES For Exercises 5 and 6, use the following information.

Gordon made a photocopy of a page from his geometry book to enlarge one of the figures. The actual figure that he copied is shown below.

Median Altitude

30 mm 39 mm

29 mm

The photocopy came out poorly. Gordon could not read the numbers on the photocopy, although the triangle itself was clear. Gordon measured the base of the enlarged triangle and found it to be 200 millimeters.

5. What is the length of the drawn altitude of the enlarged triangle? Round your answer to the nearest millimeter.

149 mm

6. What is the length of the drawn median of the enlarged triangle? Round your answer to the nearest millimeter.

154 mm

Chapter 7

39

Glencoe Geometry

Lesson 7-5

Answers (Lesson 7?5)

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download