Similar Polygons & Scale Factor

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

Similarity Statement ABC ~ DEF

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

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

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?

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

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

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

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

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

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

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).

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

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

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

k = 1/2

k = 2

Worksheet