Geometry 6.5 SWLT: Use the SSS & SAS Similarity Theorems

Side-Side-Side (SSS) Similarity Theorem If the corresponding side lengths of two triangles are proportional, then the triangles are similar., then  ABC   RST A B C R S T

Using the SSS Theorem Which is Similar to  ABC? A B C D E F G J H

Compare the Triangles by finding the ratios of the corresponding Sides  ABC   DEF? Shortest Sides Longest Sides Remaining Sides The ratios are not the same, so  ABC is not similar to  DEF  ABC   GHJ? Shortest Sides Longest Sides Remaining Sides All ratios are equal,  ABC   GHJ

Side-Angle-Side (SAS) Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides that form these angles are proportional, then the triangles are similar If and, then  XYZ   MNP X Z Y M P N

Using SAS… is  PRQ   TSR?  PRQ and  SRT are vertical angles,  are congruent Find the Ratios of the corresponding sides Shorter Sides Longer Sides The corresponding sides proportional, so  PRQ   TRS R P Q S T