1. 5-6 Using Similar Figures Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 5-6 Using Similar Figures Warm Up Solve each problem. 1. 2.
Course 2
5-6
Using Similar Figures
Warm Up
Solve each problem. k 4 75 25 6 19 24 x 1. =
k = 12 2.
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 Z K O JN KO

3. 5-6 Using Similar Figures Problem of the Day
Course 2
5-6
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 minutes

4. 5-6 Using Similar Figures
Course 2
5-6
Using Similar Figures
Learn to use similar figures to find unknown lengths.

5. Insert Lesson Title Here
Course 2
5-6
Using Similar Figures
Insert Lesson Title Here
Vocabulary
indirect measurement

6. 5-6 Using Similar Figures
Course 2
5-6
Using Similar Figures
Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

7. Additional Example 1: Finding Unknown Lengths in Similar Figures
Course 2
5-6
Using Similar Figures
Additional Example 1: Finding Unknown Lengths in Similar Figures
Find the unknown length in similar figures. AC QS = AB QR
Write a proportion using corresponding sides. 12 48 14 w =
Substitute lengths of the sides.
12 · w = 48 · 14
Find the cross product.
12w = 672
Multiply.
12w 12
672 12 =
Divide each side by 12 to isolate the variable.
w = 56
QR is 56 centimeters.

8. Insert Lesson Title Here
Course 2
5-6
Using Similar Figures
Insert Lesson Title Here
Try This: Example 1
Find the unknown length in similar figures. x
10 cm Q R A B
12 cm
24 cm D C S T AC QS AB QR =
Write a proportion using corresponding sides. 12 24 10 x =
Substitute lengths of the sides.
12 · x = 24 · 10
Find the cross product.
12x = 240
Multiply.
12x 12
240 12 =
Divide each side by 12 to isolate the variable.
x = 20
QR is 20 centimeters.

9. Additional Example 2: Measurement Application
Course 2
5-6
Using Similar Figures
Additional Example 2: Measurement Application
A volleyball court is a rectangle that is similar in shape to an Olympic-sized swimming pool. Find the length of the pool.
Let l = the length of the pool. 9 25 18 l
Write a proportion using corresponding
side widths. =
9 ·l = 18 · 25
Find the cross products.
9l = 450
Multiply. 9l 9 =
450 9
Divide each side by 9 to isolate the
variable.
l = 50
The pool is 50 meters long.

10. Insert Lesson Title Here
Course 2
5-6
Using Similar Figures
Insert Lesson Title Here
Try This: Example 2
The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.
12 cm
6 cm
3 cm ?
Let w = the width of the right rectangle. 6 12 3 w
Write a proportion using corresponding
side lengths. =
6 ·w = 12 · 3
Find the cross products.
6w = 36
Multiply. 6w 6 = 36 6
Divide each side by 6 to isolate the
variable.
w = 6
The right rectangle is 6 cm wide.

11. Additional Example 3: Using Indirect Measurement
Course 2
5-6
Using Similar Figures
Additional Example 3: Using Indirect Measurement
City officials want to know the height of a traffic signal. The traffic
light casts a shadow that is 45 ft long. A stop sign casts a shadow
that is 30 ft long. If the stop sign is 15 ft high, what is the height of
the traffic light?
Let x = the height of the traffic light. 30 45 15 x =
Write a proportion.
30 · x = 45 · 15
Find the cross product.
30 x = 675
Multiply.
30x 30
675 30
Divide each side by 30 to
isolate the variable. =
x = 22.5
The traffic light is 22.5 feet tall.

12. Insert Lesson Title Here
Course 2
5-6
Using Similar Figures
Insert Lesson Title Here
Try This: Example 3
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
Write a proportion using corresponding side
lengths. =
8 · x = 2 · 12
Find the cross products.
8x = 24
Multiply. 8x 8 24 8 =
Divide each side by 8 to isolate the variable.
x = 3
The base of the inside triangle is 3 inches.

13. Insert Lesson Title Here
Course 2
5-6
Using Similar Figures
Insert Lesson Title Here
Lesson Quiz
Find the unknown length in each pair of similar figures. J A
3. These two rectangular
cakes are similar in shape. How long is the larger cake?
144 cm 1.
96 cm x
80 cm C K
56 cm B L
84 cm
10 in.
x = 120 cm
6 in. x 2.
9 in.
160 cm
120 cm t
72 cm
90 cm
x = 15 inches
t = 150 cm