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Geometry 6.4 – 6.5 – Prove Triangles Similar by AA, SSS and SAS Learning Target: By the end of today’s lesson we will be able to successfully prove triangles are similar using AA, SSS, and SAS postulates, where the corresponding angles are congruent and the corresponding sides are proportional. ANGLE –ANGLE (AA) SIMLARITY POSTULATE: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. ∆JKL ~ ∆XYZ 1) Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. a) b) c) 2) Show that the two triangles are similar. a) ∆RTV and ∆RQS b) ∆LMN and ∆NOP c) ∆BCD and ∆EFD SIDE-SIDE-SIDE (SSS) SIMLARITY POSTULATE: If the corresponding side lengths of two triangles are proportional then the triangles are similar. If AB BC CA , then ABC ~ RST. RS ST TR 3) Is either DEF or GHJ similar to ABC? 4) Find the value of x that makes ABC ~ DEF. SIDE-ANGLE-SIDE (SAS) SIMLARITY POSTULATE: If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are ___________________, then the triangles are similar. If X M and ZX XY , then XYZ MNP. PM MN 5) A lifeguard is standing beside the lifeguard chair on a beach. The lifeguard is 6 feet 4 inches tall and casts a shadow that is 48 inches long. The chair casts a shadow that is 6 feet long. Are the triangles similar? If so, how tall is the chair? 90ooo Triangle Similarity Postulate and Theorems: AA Similarity Postulate: If A D and B E, then ABC ~ DEF. (If 2 angles of 1 triangle = 2 angles of another triangle they are similar) SSS Similarity Theorem: If AB BC AC , then ABC ~ DEF. DE EF DF (If all sides of 1 triangle are proportional to all sides of another triangle they are similar) SAS Similarity Theorem: If A D and AB AC , then ABC DEF. DE DF (If all 2sides of 1 triangle proportional to 2 sides of another triangle and the included angles are = then the triangles are similar)