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1 of 9 © Boardworks 2015 Information 2 of 9 © Boardworks 2015 Proving triangles similar Triangles are similar when corresponding angles are congruent and corresponding sides have the same ratio. Prove that △ABC ~ △DEC. show corresponding angles are congruent: 19.7 reflexive property of congruence: ∠BAC ≅ ∠DAE corresponding angles postulate: ∠ADE ≅ ∠ABC ∠AED ≅ ∠ACB 26.3 35.3 16.9 15.6 28.0 show corresponding sides have the same ratio: AE/AC = 28.0/(28.0+15.6) = 0.64 AD/AB = 35.3/(35.3+19.7) = 0.64 3 of 9 DE/BC = 16.9/26.3 = 0.64 © Boardworks 2015 Using similarity in triangles 4 of 9 © Boardworks 2015 Exploring similarity postulates 5 of 9 © Boardworks 2015 Establishing the AA similarity postulate Angle-angle similarity postulate: If two angles of a triangle are congruent to two angles of another triangle, then the two triangles are similar. ● If two triangles are similar, they are related by similarity transformations. ● Rotation, reflection and transformation preserve angles and side lengths. ● Dilation preserves angle but changes the sides lengths proportionally. ● If two angles of a triangle are specified, the third one is also determined. ● Therefore, two triangles with two congruent angles are similar. 6 of 9 © Boardworks 2015 Similar triangles 7 of 9 © Boardworks 2015 Summary activity 8 of 9 © Boardworks 2015 Want to see more? This is only a sample of one of hundreds of Boardworks Math presentations. To see more of what Boardworks can offer, order a full presentation completely free: www.boardworkseducation.com/highschoolmathpresentation 9 of 9 © Boardworks 2015