GeometrySections 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.

Shortest sides Longest sides Remaining sides

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

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