1. Goal
Identify and use similar triangles

2. W is reflexive and both triangles have a right  .
Angle-Angle (AA) ~ Postulate If two corresponding angles are congruent, then the triangles are similar. W X V Y Z
W is reflexive and both triangles have a right  .
ΔWVX ~ ΔWZY by AA ~ Post.

3. Side-Side-Side (SSS) ~ Theorem
If the lengths of the 3 corresponding sides of two triangles are proportional, then the triangles are similar.
Side-Angle-Side (SAS) ~Theorem
If the lengths of 2 corresponding sides are proportional and the included angles are congruent , then the triangles are similar.

4. Prove the triangles are similar.

5. Using the SSS Similarity Theorem
Which of these
three triangles
are similar?
1. Compare ratios of side lengths of ΔABC and ΔDEF
shortest sides longest sides remaining sides
Because the ratios are all equal, ΔABC ~ ΔDEF.
2. Compare ratios of side lengths of ΔABC and ΔGHJ
Because the ratios are not equal, ΔABC and ΔGHJ are not similar.
Since ΔABC ~ ΔDEF and ΔABC is not ~ ΔGHJ,
ΔDEF is not ~ ΔGHJ.

6. AC = 6, AD = 10, BC = 9, BE = 15. Describe how to prove that ΔACB ~ ΔDCE.
CD = ? EC= ? Show that corresponding sides are proportional. Then use SAS Similarity with vertical angles ACB and DCE.