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Proving Triangles Similar through SSS and SAS CH 6.5 Side Side Side Similarity Theorem • If the corresponding side lengths of 2 triangles are proportional, then the triangles are similar To prove 2 triangles similar using SSS • In order to prove similarity using SSS, you must check each possible proportion of the side lengths of a triangle. Not similar Use SSS to find the Scale Factor and determine whether the triangles are similar…if they are similar name the triangles correctly ∆ ABC ~∆DEF AC 9 3 DF 6 2 BC 15 3 EF 10 2 AB 12 3 DE 8 2 Use SSS to find the Scale Factor and determine whether the triangles are similar Not Similar AB DE 5 4 AC DF 8 7 BC EF 7 6 Assuming that ∆ ABC~ ∆ DEF find x. Each proportion will equal the scale factor AB AC BC DE DF EF 8 4 = 3( x 1) 12 4(3x+3) = 8(12) 12x + 12 = 96 12x = 84 x = 7 Assuming that ∆ XYZ~ ∆ PQR find x. Each proportion will equal the scale factor XY XZ YZ PQ PR QR 20 2 30 3 3(12) = 2(3x -6) 2 12 36 = 6x -12 3 3( x 2) 48 = 6x x = 8 Side Angle Side Similarity Theorem • If 2 triangles have a corresponding congruent angle and the sides including that angle are proportional, then the 2 triangles are similar. Are the Triangles similar? How? yes SAS Name the corresponding Side, Angle, and Side for each triangle BC 9 3 AC 18 3 ACB DCE CE 15 5 CD 30 5 Are the Triangles similar? How? yes SAS Name the corresponding Side, Angle, and Side for each triangle Find the scale factor to back it up RT 28 4 SR 24 4 R N NQ 21 3 PN 18 3 Are the Triangles similar? How? yes SAS or SSS Name the corresponding Side, Angle, and Side and Side, Side, Side for each triangle. Find the scale factor to back it up WX 20 4 WZX XZY XZ 12 4 WZ 16 4 XY 15 3 ZY 9 3 XZ 12 3 Find the Scale Factor and determine whether the triangles are similar using SAS ∆ RST ~ ∆ XYZ S Y RS 4 2 XY 6 3 ST 6 2 YZ 9 3 Is there enough information to determine whether the triangles are similar? no Why? The sides are not proportional and it does not follow SAS. Is there enough information to determine whether the triangles are similar? yes Which Similarity Postulate allows us to say yes? SAS CD CG C C CE CF 15 20 27 36 5 5 9 9 Are the triangles similar? Which similarity postulate allows us to say it is similar? yes SAS The sides are proportional and the included angles are congruent. Are the triangles similar? Which similarity postulate allows us to say it is similar? yes SAS 2 sides are proportional and the included angle is congruent. Assuming that these triangles are similar. Let’s solve for the missing variables. 3x + 8 13y - 38 12 4x - 5 15 6y + 11 Page 391 • #3- 9, 15 - 23