1. Similar Polygons & Scale Factor

2. Similar Polygons 1. Corresponding angles are congruent
2. Corresponding sides are proportional

3. Similarity Statement
ABC ~ DEF

4. Solve for x and y. x = 26 cm y = 12 cm L A 5 cm x S 10 cm y 13 cm C BT
x = 26 cm
y = 12 cm

5. ABCD ~ EFGH. Solve for x. G H D C x 27 A B 6 F E 18
x = 9

6. Ex. A tree cast a shadow 18 feet long
Ex. A tree cast a shadow 18 feet long. At the same time a person who is 6 feet tall cast a shadow 4 feet long. How tall is the tree?

7. Ratio of Similar Polygons
12/30/2018
Ratio of Similar Polygons
Corresponding Sides : Corresponding Sides Or
Perimeter : Perimeter
A : B

8. Ratio of Similar Polygons
12/30/2018
Ratio of Similar Polygons
Area : Area
A2 : B2

9. Ratio of Similar Polygons
12/30/2018
Ratio of Similar Polygons
Volume: Volume
A3 : B3

10. The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides.
The ratio of the perimeters of CAT to DOG is 3:2
Find the value of y. A
C T O
D G 4 10 y
y = 4

11. Find the perimeter of the smaller triangle.
12 cm
4 cm
Perimeter = x
Perimeter = 60 cm
x = 20 cm

12. Scale Factor – the ratio of a new image to its original image
The ratio of corresponding sides

13. Scale Factor
When scale factor is greater than 1, the shape gets bigger (enlargement).
When scale factor is less than 1, but greater than 0, the shape gets smaller (reduction).

14. SCALE FACTOR. 6 2
new
original 7 14 10 5
original
new 3 6

15. All you do is multiply k to (x, y).
Find the coordinates of the dilation image for the given scale factor, k.
Example 1:
G(0, -2), H(1, 3), and I(4, 1); k = 2
All you do is multiply k to (x, y).
G’( , ), H’( , ), and I’( , )
0 -4
2 6
8 2

16. All you do is multiply k to (x, y).
Find the coordinates of the dilation image for the given scale factor, k.
Example 2:
L(8, -8), N(0, 16), and M(4, 5); k = 1/4
All you do is multiply k to (x, y).
L’( , ), N’( , ), and M’( , )
2 -2
0 4
1 5/4

17. k = 1/2

18. k = 2

19. Worksheet