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MPM2D U06L01 Congruent and Similar Triangles When comparing 2 triangles, they are either: congruent, similar or neither 1) Congruent Triangles: have the exact same Size and Shape ( ) ALL CORRESPONDING SIDES AND ANGLES ARE EQUAL 2) Similar Triangles: have the same SHAPE but are DIFFERENT sizes (one triangle is an enlargement or reduction of the other). The symbol used to indicate similarity is ~ PROPERTIES OF SIMILAR TRIANGLES D A 6 cm 2 cm B 4 cm 12 cm 4 cm C E 8 cm F Δ If ABC and DEF are similar... Δ i) the corresponding pairs of angles are equal ii) the ratios of the corresponding sides are equal iii) the ratios of the areas is equal to the ratio of their squares of their corresponding sides MPM2D U06L01 CONDITIONS FOR SIMILARITY A D B F C E i) SSS: 3 pairs of corresponding sides are proportional ii) SAS: 2 pairs of corresponding sides are proportional and the contained angles are equal iii) AA~: 2 pairs of corresponding angles are equal Example # 1: a) Show that ABC EDC. Δ Δ To demonstrate similarity; SSS~ not enough information SAS~ not in this situation AA~ use this one b) Find the lengths of x and y. A 7 cm B statement 4 cm 5 cm authority opposite angle theorem C 6 cm D x y parallel line theorem alternate angles (Z pattern) E Because they are similar, the corresponding sides must be proportional. parallel line theorem alternate angles (Z pattern) Homework: p. 460 # 1 - 4 , 5ac , 6ac , 7ac , 10