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Lesson 7-3 D Objective – To prove triangles similar using AA, SSS, and SAS. AA Postulate If two angles of one triangle are congruent to two angles of another, then the triangles are similar. Z B A C X Y B Given: BC DE Prove: ABC ADE A Statement C E Reasons 1) BC DE Given 2) BCA DEA Corres. s Postulate 3) A A Reflexive Prop. of 4) ABC ADE AA Simlarity ABC X ZY SSS Similarity If three sides of one triangle are proportional to three corresponding sides of another triangle, then the triangles are similar. E B 9 9 A C 12 AB 9 3 ED 12 4 BC 9 3 DF 12 4 AC 12 3 EF 16 4 D F 12 12 M P by Alternate Interior s Thm. MN = LN 10 = x PN NO 12 15 ABC E D F 150 12x E B C D 15 AB 6 2 DE 9 3 ABC DEF F x 12.5 Explain how to find x. B 8 A 9 AC 10 2 DF 15 3 N MNL PNO by AA Similarity. 6 10 x L O 15 10 MNL PNO by Reflexive Prop of . SAS Similarity If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are congruent. A M P 16 12 Explain how to find x. D 4 6 12 C 6 x E It is given in the drawing, AB 8 2 , and AD 12 3 AB AC by substitution. AD AE A A by Reflexive Prop of . ABC ADE by SAS Similarity. A D Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 AC 12 2 . AE 18 3 12 6 18 x 12x 108 x 9 1 Lesson 7-3 If each pair of triangles is similar, explain why. If each pair of triangles is similar, explain why. 1) 5) 2 3) 6 8 4 3 12 6 Similar by AA Similarity. 2) 9 6 12 7) 4 3 12 9 8 4 , 12 4 10 5 15 5 Similar by SAS Similarity. 20 4) 3 15 12 4 , 9 3 , 6 2 15 5 12 4 9 3 Not Similar 3 20 Similar by AA Similarity. 6) 12 12 10 5 12 3 , 3 20 5 5 Similar by SSS Similarity. Similar by AA Similarity. 8) 5 6 12 10 Not Similar 5 5 6.25 4 5 4 6.25 5 Similar by SAS Similarity. Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 2