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are triangles that have the same size and shape. Congruent triangles ? Similar triangles ? have the same shape but different sizes. Similar Triangles ? Congruent Triangles ? How do we know when triangles are similar? Their corresponding angles have to be Their corresponding sides have to be 2 5 4 1 2.5 2 proportional ? congruent ? The triangles shown are similar. Find the ratio ofthe corresponding sides of the triangles.Simplify to a whole number if possible. 3 7.5 6 1 2.5 2 31 = The triangles shown are similar. Find the ratio ofthe corresponding sides of the triangles.Simplify to a whole number if possible. 3 7.5 6 1 2.5 2 6 2 = The triangles shown are similar. Find the ratio ofthe corresponding sides of the triangles.Simplify to a whole number if possible. 3 7.5 6 1 2.5 2 7.52.5 = These triangles are similar. Solve for x. 2 5 x 20 5x = x 2 Solve x = = 5 The Angle-Angle Similarity Postulate is one way to prove that two triangles are similar. If two angles of one triangle are congruent to two anglesof another triangle, then the triangles are similar! We use matching arc marks to indicate congruent angles. What is the abbreviation we use for Angle-Angle similarity? Angle Angle AA ? ASA AAS HL Complete the similarity statement. The order of the letters matter! AA Similarity Postulate:If two angles of one triangle are congruent to two anglesof another triangle, the triangles are similar. R T S F ∆RST ~ ∆ E G The triangles shown in the picture are: )) 10 congruent by AA similar by AA not similar not enough information 5 )) The triangles shown in the picture are: similar by AA because two angles are congruent not similar by AA because only one pair of angles are shown as congruent. 10 6 5 3 Interpret the diagram and identify the congruent angles. ∠A ≅ ∠ ∠B ≅ ∠ ∠C ≅ ∠ E ? D ? C ? Write a similarity statement. ΔBAC ≅ Δ ∠A ≅ ∠E ∠B ≅ ∠D ∠C ≅ ∠C |