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Similarity and Congruence Learning Outcomes Know when shapes are similar Know when shapes are congruent Use similarity to find the missing sides of 2-D shapes Use congruency to find the missing sides of triangles Compare areas and volumes of similar shapes Similar Triangles Similarity and Congruence Similar triangles – all angles are the same, sides of different lengths but in constant ratio E B A C F D Triangles ABC and DEF are similar because: Bˆ Eˆ Aˆ Dˆ Cˆ Fˆ by subtraction Ratio of sides = DF = EF AC BC Similar Triangles Similarity and Congruence Triangles ABC and DEF are similar Find i) AC ii) DE E B y 4 A 9 6 x C D 5 F Similar Triangles Similarity and Congruence P Find x 1.5 X 4.5 R 3 Y x Q Similarity and Congruence 1) Comparing Areas & Volumes of Similar Shapes 2m 1m x 2) 5 32cm2 The above two rectangles are similar. i) If the above area of the smaller rectangle is 20m2 find the area of the larger rectangle. ii) If the area of the larger is 40m2, find the area of the smaller. 50cm2 The above two rectangles are similar. Find x. Similarity and Congruence 3) Comparing Areas & Volumes of Similar Shapes The sides of two cubes are in the ratio 2 : 5 i) Write down the ratio of their area ii) Write down the ratio of their volume iii) Find the volume of the larger if the volume of the smaller cube is 10cm3 Summary Length Ratio Area Ratio Volume Ratio a:b a2 : b2 a3: b3 Similarity and Congruence Additional Notes Similarity and Congruence Learning Outcomes: At the end of the topic I will be able to Know when shapes are similar Know when shapes are congruent Use similarity to find the missing sides of 2-D shapes Use congruency to find the missing sides of triangles Compare areas and volumes of similar shapes Can Do Revise Further