Triangle Similarity

Two Triangles are similar if : AA ~ : two pairs of corresponding angles are congruent, SSS~ : all three pairs of corresponding sides are proportional, or SAS~ : two pairs of corresponding sides are proportional and their included angles are congruent.

AA ~ If 2 corresponding angles are congruent then the 3rd pair of corresponding angles must be congruent also. (Angle sum of a triangle = 180°.) A 65° 49° A’ 65° 49°

SSS~ = = AB BC AC A’B’ B’C’ A’C’ You should be able to identify a scale factor. = = A B C 15 9 12 A’ 9 12 15 4.5 6 7.5 = 7.5 4.5 B’ C’ Scale factor is 2 to 1 or 1/2 6

SAS~ The included angles are the angles that are formed by the two pairs of corresponding sides. A 65° C 9 12 A’ 4.5 65° C’ 6

A Postulate is a statement that is accepted to be true without PROOF. POSTULATES AA~ SSS~ SAS~ A Postulate is a statement that is accepted to be true without PROOF.

What did you discover with your triangle cutting exercise? (cut parallel to C’T’) T C A Do NOT cut this original Triangle. A’ C’ T’ T’’’ C’’’ A’’’ A’’ C’’ T’’

Hopefully… Corresponding angles are @ Corresponding sides are proportional Regardless of where you make your cut.

Side-Splitting Theorem A line parallel to one side of a triangle divides the other two sides proportionally. 4 3 8 10 2/3

How many ratios do you see? 4 3 8 10 2/3

How many ratios do you see? 4 3 8 10 2/3 3 8 11 4 10 2/3 14 2/3 = =