Prove Triangles Similar by SSS and SAS Geometry Sections 6.5 Prove Triangles Similar by SSS and SAS

Side-Side-Side (SSS) Similarity Theorem (Theorem 6.2) If the corresponding side lengths of two triangles are proportional, then the triangles are similar

Example 1: Is either ∆ DEF or ∆ GHJ similar to ∆ ABC? Step 1: Compare ∆ ABC and ∆ DEF by finding ratios of corresponding side lengths. Shortest sides Longest sides Remaining sides Step 2: Compare ∆ ABC and ∆ GHJ by finding ratios of corresponding side lengths.

Example 2: Find the value of x that makes triangle ABC ~ triangle DEF.

Example 2 (Con’t): Find the value of x that makes triangle ABC ~ triangle DEF.

Side-Angle-Side (SAS) similarity Theorem (Theorem 6.3) If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar

Use the SAS Similarity Theorem Example 4: Example 5: Is ∆ FDM ~ ∆AVQ? Is ∆ GHK ~ ∆ NMK? YES YES

Examples Page 391-393: 4-10 All, 15, 18-23