Transcript Slide 1
5-8 Using Similar Figures
Course 2
5-8 Using Similar Figures Warm Up
Solve each proportion.
1.
k
4 = 75 25 k = 12
2
. 6 = 24 x = 76 Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles.
3.
J A N JN Z K KO O
Course 2
5-8 Using Similar Figures Problem of the Day
Harvey starts to fill a 3-gallon tank from a hose that delivers 1 gallon per minute. However, the tanks leaks 1 quart per minute. In how many minutes will the tank begin to overflow?
4 Course 2
5-8 Using Similar Figures
Learn
to use similar figures to find unknown lengths.
Course 2
5-8
Vocabulary
indirect measurement
Course 2
5-8 Using Similar Figures
Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.
Course 2
5-8 Using Similar Figures Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown length in similar figures.
AC QS
12 48 =
AB QR
12 · w = 48 · 14 12w = 672 12w 12 = 672 12 w = 56
Write a proportion using corresponding sides.
Substitute lengths of the sides.
Find the cross product.
Multiply.
Divide each side by 12 to isolate the variable.
QR is 56 centimeters.
Course 2
5-8 Check It Out: Example 1 Find the unknown length in similar figures.
10 cm
x A B Q R
12 cm 24 cm
C D S T
AC QS
12 24 =
AB QR
12 · x = 24 · 10 12x = 240 12x 12 = 240 12 x = 20
Write a proportion using corresponding sides.
Substitute lengths of the sides.
Find the cross product.
Multiply.
Divide each side by 12 to isolate the variable.
QR is 20 centimeters.
Course 2
5-8 Additional Example 2: Measurement Application 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 8 · x = 2 · 12 8x = 24
Write a proportion using corresponding side lengths.
Find the cross products.
Multiply.
8x 8 = 24 8 x = 3
Divide each side by 8 to isolate the variable.
The base of the inside triangle is 3 inches.
Course 2
5-8 Check It Out: Example 2 The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.
6 cm 12 cm 3 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
Write a proportion using corresponding side lengths.
Find the cross products.
Multiply.
Divide each side by 6 to isolate the variable.
The right rectangle is 6 cm wide.
Course 2
5-8 Using Similar Figures 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 ft 48.75 ft h ft 27.25
15 27 15 ≈ 49
h
9 5 9h ≈ 245 h ≈ 27
Write a proportion.
Use compatible numbers to estimate.
Simplify.
Cross multiply.
Multiply each side by 9 to isolate the variable.
The traffic light is about 30 feet tall.
Course 2
5-8 Using Similar Figures Check It Out: Example 3
The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle.
14.75 ft 30.25 ft
5
ft h ft 5 14.75
=
h
30.25
5 15 ≈ h 30 1 3 1 • 30 ≈ 3 • h 30 ≈ 3h 10 ≈ h
Write a proportion.
Use compatible numbers to estimate.
Simplify.
Cross multiply.
Multiply each side by 5 to isolate the variable.
The outside triangle is about 10 feet tall.
Course 2
5-8 Lesson Quiz: Part I Find the unknown length in each pair of similar figures.
1.
x = 120 cm
2.
t = 150 cm
Course 2
5-8 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.
Course 2
x = 15 inches