8.2 Similarity Objective: After studying this section, you will be able to identify the characteristics of similar figures.

Similar—figures with the same shape but not necessarily the same size. Dilation—enlargement of an object. Reduction—opposite of dilation, creates a smaller similar object of the original object.

A pinhole camera produces a reduced image of a candle A pinhole camera produces a reduced image of a candle. The size of the image is proportional to the distance of the candle from the camera. Given the measurements shown in the diagram, find the height of the candle. 20 cm 2 cm H 5 cm

Definition Similar Polygons are polygons in which 1. The ratios of the measures of corresponding sides are equal 2. Corresponding angles are congruent

Triangle MCN is a dilation of triangle MED, with an enlargement ratio of 2:1 for each pair of corresponding sides. Find the lengths of the sides of triangle MCN C (0,8) E (0,4) (0,0) (3,0) (6,0) M D N

Given ABCD is similar to EFGH with measures shown 6 4 9 A C 7 E 3 G D Find FG, GH, and EH H

Theorem. The ratio of the perimeters. of two similar polygons Theorem The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides

Given triangle JHK is similar to triangle POM, Find x and y M K J H O P

Given: Triangle BAT is similar to Triangle DOT, OT = 15, BT = 12, TD = 9 Find the value of x (AO) x O 15 B D 12 T 9

C P C’ In the diagram, segments PA, PB, and PC are drawn to the vertices of triangle ABC from an external point P, then extended to three times their original lengths to points A’, B’, and C’. What are the lengths of the sides of triangle A’B’C’? 15 10 B A 12 A’ B’

Summary: Explain the difference between similar and congruent polygons. Homework: worksheet