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Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem. Use similar triangles to solve problems. Similar Triangles Angle-Angle (AA) Similarity If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. 75 48 JKL ~ QPM By AA similarity. R W alt int . X T alt int . SRX ~ SWT By AA similarity Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. 46 43 No triangles are not similar since there are no 2 angles the same. L L LJK LPQ JKL ~ PQL By AA similarity Theorem Side-Side-Side (SSS) Similarity If the corresponding side lengths of two triangles are proportional, then the triangles are similar. Theorem Side-Angle-Side (SAS) Similarity If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. Determine whether the triangles are similar. If so, write a similarity statement. Explain. 6 8 5 15 20 12.9 0.4 = 0.4 0.4 = 0.4 0.4 = 0.4 PQR ~ STR By SSS similarity Determine whether the triangles are similar. If so, write a similarity statement. Explain. 8 12 16 6 9 12 A. Uses SAS similarity C. Uses AA similarity D. Uses SSS similarity B. Does not have a congruent included angle. No similarity B is the only choice that satisfies a similarity condition. SSS similarity. Determine whether the triangles are similar. If so, write a similarity statement. Explain. 8 10 12 15 A A AEF ~ ACB By SAS Similarity Find BE and AD side 3 x Whole of one triangle to whole side 5 3.5 of other triangle. 10.5 = 5x 2.1 = x 3 y 5 y3 3y + 9 = 5y 9 = 2y 4.5 = y BE = 2.1 AD = 4.5 + 3 = 7.5 Find QP and MP 5 6 5 x 633 5 48 = 30 + 6x 18 = 6x 3=x QP = 3 MP = 5 + 3 = 8 QP = 3 MP = 8 Find WR and RT x6 8 2 x 6 10 10x + 60 = 16x + 48 12 = 6x 2=x WR = x + 6 = 8 RT = 2x + 6 = 10 Real world Adam is standing next to the Palmetto Building in Columbia, South Carolina. He is 6 feet tall and the length of his shadow is 9 feet. If the length of the shadow of the building is 322.5 feet, how tall is the building? 6 x 9 322.5 9x = 1935 x = 215 The Palmetto building is 215 feet tall. Homework Pg. 479 1 – 8 all, 10 – 24 E, 38, 42 – 56 E