1. C 5 4 A B 6 Z 10 8 X Y 12

2. Exercise 6 in. ∆XYZ ~ ∆LMN. Dimensions are in inches. Find LM. M Y 1216 P L N
9.6 10 W X Z 20 2

3. Exercise 4.8 in. ∆XYZ ~ ∆LMN. Dimensions are in inches. Find MP. M Y12 16 P L N
9.6 10 W X Z 20

4. Exercise
What is the ratio of the perimeter of ∆XYZ to the perimeter of ∆LMN?
2 : 1 10 L M N 20 X Y Z 16 12
9.6

5. Exercise
Find the area of of ∆LMN.
24 in.2 10 L M N 20 X Y Z 16 12
9.6

6. Exercise
What is the ratio of the area of ∆XYZ to the area of ∆LMN?
4 : 1 10 L M N 20 X Y Z 16 12
9.6

7. Ratio of the Perimeters of Similar Polygons
The ratio of the perimeters is equal to the ratio of the corresponding sides.

8. Example 1
The corresponding sides of two similar triangles are 16 in. and 12 in. The perimeter of the first triangle is 55 in. Find the perimeter of the second triangle, p2.
16 12 =
4 3

9. 16 12 =
4 3
4 3 =
55 p2
4p2 = 3(55)
4p2 = 165 4
p2 = in.

10. Example 2
The perimeters of two similar hexagons are 20 ft. and 180 ft. The smaller hexagon has one side of 2 ft. Find the corresponding side of the larger hexagon.
2 s =
20 180

11. 2 s =
20 180
2 s =
1 9
s = 2(9)
s = 18 ft.

12. Example For the figure, write the missing factor: EF = __BC. 3 D A B C4 12 3

13. 4 6 4a 6a

14. Ratio of the Areas of Similar Polygons
The ratio of the areas of similar polygons is equal to the ratio of the squares of the corresponding sides.

15. Example 3
The first of two regular pentagons has a side of 4 cm, and the second has a side of 3 cm. What is the ratio of their areas?
4 3 2
4 3
4 3
16 9
( ) = × =

16. Example 4
The first of two similar polygons has a side of 3 cm and an area of 10 cm2. The corresponding side of the second is 5 cm. What is the area of the second polygon?
( )
10 A2 =
3 5 2

17. 10 A2 =
9 25
9A2 = 10(25)
9A2 = 250 9
A2 ≈ 27.8 cm2

18. Example 5
The areas of two similar pentagons are 400 mm2 and 100 mm2. One side of the smaller pentagon is 9 mm. Find the length of the similar side of the larger pentagon.
( )
s 9 = 2

19. 4 1 =
s2 81
s2 = 4(81)
s2 = 324
s = 324
s = 18 mm

20. Example
∆ABC ~ ∆DEF. For the figure, write the missing factor: area of ∆DEF = __ area of ∆ABC. D A B C E F 4 12 9

21. Example
∆ABC ~ ∆DEF. If the area of ∆ABC is 8 units2, what is the area of ∆DEF? D A B C E F 4 12
72 units2

22. Example
∆ABC ~ ∆DEF. If the perimeter of ∆ABC is 14 units, what is the perimeter of ∆DEF? D A B C E F 4 12
42 units

23. Example
There are 640 acres in a square mile. How many acres are in a parcel of land that is mi. × mi.?
1 2
1 2
160 acres

24. Example
How many square inches are in a rectangle that is 2 ft. × 3 ft.?
864 in.2

25. Example
How many square feet are in 288 in.2?
2 ft.2

26. Example
How many square feet are in a square yard? How many square inches are in a square yard?
9 ft.2; 1,296 in.2