Geometry 7.2 SWLT: Use Proportions to identify similar polygons

Similar Polygons Two or more polygons are similar, if corresponding angles are congruent and corresponding side lengths are proportional Same as when comparing and proving congruency, order is important.

 ABC   DEF  List all pairs of Congruent Angles  A   D,  B   E,  C   F 2. Confirm that the ratios of the corresponding side lengths are equal.  Write the ratios of the corresponding side lengths in a statement of proportionality A B C D E F

 BCD   RST, Find the value of x Write a Proportion Substitute Cross Multiply Solve for x B C D R S T x 10 12x = 13(24) 12x = 312 x = 26

Theorem: Areas of Similar Polygons If two polygons are similar, then the ratio of their areas are equal to the ratios of their corresponding sides. If KLMN  PQRS, then… 15(8) = 24PQ 120 = 24PQ PQ = 5 KL MN PQ RS 8 A = 24 A = 15