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SIMILARITY THEOREMS Similarity in Triangles Angle-Angle Similarity Postulate (AA~)If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. W S 45 R V 45 B WRS BVS because of the AA~ Postulate. Similarity in Triangles Side-Angle-Side Similarity Postulate (SAS~)- If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the angles are proportional, then the triangles are similar. 16 C T 32 32 28 12 E U P 21 TEA CUP because of the A SAS~ Postulate. The scale factor is 4:3. Similarity in Triangles Side-Side-Side Similarity Postulate (SSS~)- If the corresponding sides of two triangles are proportional, then the triangles are similar. A 30 15 B C Q20 ABC QRS 3 because of the R S 4 SSS~ Postulate. The scale factor is 1:5. 6 Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. F J H G K Yes, FGH KJH because of the AA~ Postulate Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. M G 3 6 O H R 10 No, these are not similar because 4 I Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. A 20 X 25 25 Y 30 B No, these are not similar because C Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. A 2 3 P 5 B J 3 3 8 C Yes, APJ ABC because of the SSS~ Postulate. Explain why these triangles are similar. Then find the value of x. 4.5 5 x 3 These 2 triangles are similar because of the AA~ Postulate. x=7.5 Explain why these triangles are similar. Then find the value of x. 5 x 110 70 3 3 These 2 triangles are similar because of the AA~ Postulate. x=2.5 Explain why these triangles are similar. Then find the value of x. x 24 14 22 These 2 triangles are similar because of the AA~ Postulate. x=12 Explain why these triangles are similar. Then find the value of x. 6 9 2 x These 2 triangles are similar because of the AA~ Postulate. x= 12 Explain why these triangles are similar. Then find the value of x. 4 5 x 15 These 2 triangles are similar because of the AA~ Postulate. x=8 Explain why these triangles are similar. Then find the value of x. x 7.5 12 18 These 2 triangles are similar because of the AA~ Postulate. x= 15 Please complete the Ways to Prove Triangles Similar Worksheet. Similarity in Triangles Side Splitter Theorem - If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides You can either proportionally. use T x or S 16 R 5 U 10 V Theorem If three parallel lines intersect two transversals, then the segments intercepted are proportional. c d a b Theorem Triangle Angle Bisector Theorem -If a ray bisects an angle of a triangle, then it divides the opposite side on the triangle into two segments that are proportional to the other two sides of the triangle. A C D B Please complete pg. 449: 1-24, 31-33.