Course 2 5-8 Using Similar Figures Do Now Test Friday on chapter5 section 1-8 Solve each proportion. 1. k4k4 = 75 25 2.2. 6 19 = 24 x 3. Triangles JNZ

Course 2

5-8 Using Similar FiguresDo Now Test Friday on chapter5 section 1-8

Solve each proportion.

1. k4

= 7525

2. 619

= 24x

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

EQ: How do I use similar figures to find unknown lengths?

Course 2

5-8 Using Similar Figures

M7G3.a Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts; M7G3.b Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures

Open Textbook to page 302-303, work quietly on #1-8 and 13-15

On #1-8, I need your corresponding sides and angles along with the ratios!

Vocabulary

indirect measurement

Insert Lesson Title Here

Course 2


Course 2


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

Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.

Additional Example 1: Determining Whether Two Triangles Are Similar

Course 2

5-7 Similar Figures and Proportions

A C

B

10 in

4 in 7 in D

E

F

16 in 28 in

40 in

AB corresponds to DE.

BC corresponds to EF.

ABDE

=? BC

EF=? AC

DF4

167

281040

14

14

14

Since the ratios of the corresponding sides are equivalent, the triangles are similar.

Write ratios using the corresponding sides.

Substitute the length of the sides.

Simplify each ratio.

=? =?

AC corresponds to DF.

=? =?

Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.

Additional Example 1: Determining Whether Two Triangles Are Similar

Course 2

5-7 Similar Figures and Proportions

A C

B

X in

3 in 6 in D

E

F

15 in 30 in

40 in

AB corresponds to DE.

BC corresponds to EF.

ABDE

= BCEF

= ACDF

AC corresponds to DF.

Find the unknown length in similar figures.

Additional Example 1: Finding Unknown Lengths in Similar Figures

ACQS

= ABQR Write a proportion using corresponding sides.

1248

= 14w

Substitute lengths of the sides.

12 · w = 48 · 14 Find the cross product.12w = 672 Multiply.

12w12

= 67212

w = 56

QR is 56 centimeters.

Divide each side by 12 to isolate the variable.

Course 2


Check It Out: Example 1


Course 2


A B

C D

10 cm

12 cm

Q R

S T

24 cm

ACQS

= ABQR

Write a proportion using corresponding sides.

1224

= 10x

Substitute lengths of the sides.

12 · x = 24 · 10 Find the cross product.

12x = 240 Multiply.

12x12

= 24012

x = 20

QR is 20 centimeters.


Find the unknown length in similar figures.x

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


Course 2


Let x = the base of the inside triangle.

82

=12x

8 · x = 2 · 128x = 24

8x8

= 248

x = 3The base of the inside triangle is 3 inches.

Write a proportion using corresponding sidelengths.

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.


Course 2


3 cm

6 cm12 cm

Let w = the width of the right rectangle.

612

= 3w

6 ·w = 12 · 3

6w = 36

6w6

= 366

w = 6

The right rectangle is 6 cm wide.

Write a proportion using correspondingside lengths.

Find the cross products.Multiply.


?

Additional Example 3: Estimating with Indirect Measurement

Course 2


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

27.2515

= 48.75h

Write a proportion.

Use compatible numbers to estimate.

95

≈ 49h

Simplify.

9h ≈ 245

The traffic light is about 30 feet tall.

27.25 ft

48.75 ft

h ft 2715

≈ 49h

Cross multiply.

h ≈ 27 Multiply each side by 9 to isolate the variable.


Course 2


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

514.75

= h30.25

Write a proportion.

Use compatible numbers to estimate.

13

≈ h30

Simplify.

1 • 30 ≈ 3 • h

The outside triangle is about 10 feet tall.

14.75 ft

30.25 ft

h ft

515

≈ h30

30 ≈ 3h Multiply each side by 5 to isolate the variable.

5 ft

Cross multiply.

10 ≈ h

Additional Example 1: Geography Application

Triangles ABC and EFG are similar.

Triangles ABC and EFG are similar. Find the length of side EG.

B

A C

3 ft

4 ft

F

E G

9 ft

x

The length of side EG is 12 ft.


Triangles DEF and GHI are similar.

Triangles DEF and GHI are similar. Find the length of side HI.

2 in

E

D F

7 in

H

G I

8 in x

The length of side HI is 28 in.

A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree?

1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river?

2. A yardstick casts a 2-ft shadow. At the same

time, a tree casts a shadow that is 6 ft long. How

tall is the tree?

7.98 m

9 ft

w

7 m5 m

5.7 m

TOTD

Find the unknown length in each pair of similar figures.


Course 2


1.

2.

x = 120 cm

t = 150 cm

TOTD

Find the unknown length in each pair of similar figures.


Course 2


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.

x = 15 inches

Documents

Course 2 5-8 Using Similar Figures Do Now Test Friday on chapter5 section 1-8 Solve each proportion. 1. k4k4 = 75 25 2.2. 6 19 = 24 x 3. Triangles JNZ