4-9 Using Similar Figures - Wild About Math!hammondzone.weebly.com/.../similar_figures_notes_ppt_2.pdf4-9 Using Similar Figures Warm Up Solve each proportion. 1. k 4 = 75 25 2. 6 19

4-9 Using Similar Figures

Warm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes


Warm Up

Solve each proportion.

1. k 4

= 75 25

2. 6 19

= 24 x

3.

Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles.

J

N Z K O

A

JN KO

k = 12 x = 76


I can use similar figures to find unknown

lengths.


Vocabulary

indirect measurement


Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.


Find the unknown measures in the similar figures.

Additional Example 1: Finding Unknown Lengths in

Similar Figures

AB JG

= BC HG Write a proportion using corresponding sides.

10 5

= 6 x

Substitute lengths of the sides.

10 · x = 5 · 6 Find the cross product.

10x = 30 Multiply.

10x 10

= 30 10

x = 3

HG is 3 centimeters.

Divide each side by 12 to isolate the variable.

H B A

C G J

10 cm

6 cm 116 cm

5.8 cm x

5 cm

31°

59°

y



Additional Example 1 Continued

Step 2 Find y.

Corresponding angles of similar triangles have equal angle measures.

H corresponds to C

y = 59

H B A

C G J

10 cm

6 cm 116 cm

5.8 cm x

5 cm

31°

59°

y



Check It Out: Example 1

AB FE

= BC DE Write a proportion using corresponding sides.

14 7

= 9 x

Substitute lengths of the sides.

14 · x = 9 · 7 Find the cross product.

14x = 63 Multiply.

14x 14

= 63 14

x = 4.5

HG is 4.5 centimeters.


D B A

C E F

14 cm

9 cm 116 cm

5.8 cm x

7 cm

27°

63°

y



Check It Out: Example 1 Continued

Step 2 Find y.

Corresponding angles of similar triangles have equal angle measures.

D corresponds to C

y = 63

D B A

C E F

10 cm

6 cm 116 cm

5.8 cm x

5 cm

27°

63°

y


The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.

Let x = the base of the inside triangle.

8 2

= 12 x

8 · x = 2 · 12

8x = 24

8x 8

= 24 8

x = 3

The base of the inside triangle is 3 inches.

Write a proportion using corresponding side lengths.

Find the cross products.

Multiply.


Additional Example 2: Measurement Application



The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.

3 cm

6 cm 12 cm

Let w = the width of the right rectangle.

6 12

= 3 w

6 ·w = 12 · 3

6w = 36

6w 6

= 36 6

w = 6

The right rectangle is 6 cm wide.

Write a proportion using corresponding side lengths.

Find the cross products.

Multiply.


?


Additional Example 3: Estimating with Indirect

Measurement

City officials want to know the height of a traffic light. Estimate the height of the traffic light.

27.25 15

= 48.75 h

Write a proportion.

Use compatible numbers to estimate.

5 3

≈ 50 h

Simplify.

5h ≈ 150

The traffic light is about 30 feet tall.

27.25 ft

48.75 ft

h ft 25 15

≈ 50 h

Cross multiply.

h ≈ 30 Divide each side by 5 to isolate the variable.



The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle.

5 14.75

= h 30.25

Write a proportion.

Use compatible numbers to estimate.

13

≈ h 30

Simplify.

1 • 30 ≈ 3 • h

The outside triangle is about 10 feet tall.

14.75 ft

30.25 ft

h ft

5 15

≈ h 30

30 ≈ 3h Divide each side by 3 to isolate the variable.

5 ft

Cross multiply.

10 ≈ h


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

Find the unknown length in each pair of similar figures.

1.

2.

x = 120 cm y = 98◦

t = 150 cm s = 120◦

33° 49°

98° y

s

19°

120° 41°


Lesson Quiz: Part II

Find the unknown length in each pair of similar figures.

3. The width of the smaller rectangular cake is 5.75 in. The width of a larger rectangular cake is 9.25 in. Estimate the length of the larger rectangular cake.

about 15 inches


1. Identify the unknown length in the given pair of similar figures.

A. x = 174 cm

B. x = 182 cm

C. x = 196 cm

D. x = 204 cm



2. Identify the unknown length in the given pair of similar figures.

A. t = 166 cm

B. t = 198 cm

C. t = 206 cm

D. t = 248 cm



3. The width of the smaller rectangular box is 6.25 inches. The width of a similar larger rectangular box is 8.75 inches. Estimate the length of the larger rectangular box.

A. about 16 in.

B. about 17 in.

C. about 18 in.

D. about 19 in.


Documents

4-9 Using Similar Figures - Wild About Math!hammondzone.weebly.com/.../similar_figures_notes_ppt_2.pdf4-9 Using Similar Figures Warm Up Solve each proportion. 1. k 4 = 75 25 2. 6 19