Warm Up –

7.3 – Similar Figures Similar Polygons – Two polygons are similar if their vertices can be paired so that: 1. Corresponding angles are congruent. 2. Corresponding sides are in proportion. Symbol for Similar: ~

P T S R Q V Z Y X W Example: 7.3 – Similar Figures Therefore – 1.  P   T   S    R   Q   2. Pent. TSRQP ~ Pent. ZYXWV VZY X W WXXYYZZV

When two polygons are similar, then the ratio of the lengths of two corresponding sides is called the Scale Factor. 7.3 – Similar Figures

B Example 1: A C KL J To determine the scale factor – match up the lengths of the corresponding sides. Reduce ratios. Scale factor of  ABC to  JKL is 3 to 1.  ABC ~  JKL ORDER MATTERS!

Example 2: 7.3 – Similar Figures A D C B E H G F z y 10 x Quad. ______ ~ Quad. ______ 1. If m  D = 92, then m  H = ____. 2. If m  C = 60, then m  G = ____. ABCDEFGH 92 60

A D C B E H G F z y x Example 2: Once you determine the scale factor, you can calculate the lengths of all of the sides of the similar figures. 7.3 – Similar Figures Scale factor of ABCD to EFGH is 2 to 3.

7.3 – Similar Figures Example 2 continued: A D C B E H G F z y x Use the scale factor of 2 to 3 to set up proportions. x = _____ y = _____ z = _____ = 3x; x = = 2y; y= = 2z; z = 12

Example 3 – Find the missing side lengths and angle measures. A C E F B D  ABC ~ Scale Factor: = x: y: y x  23  35  23  35  zz  FDE 15 to 9 5 to 3 x = 10 y = 3 zz

Example 4: Name all of the pairs of congruent angles. a.  IKJ ~ b. Find x. c. Find y. J I K L H y x  HLJ  JIK   JHL;  JKI   JLH y x