1. Similarity in Triangles

2. Similar Definition: In mathematics, polygons are similar if their corresponding (matching) angles are congruent (equal in measure) and the ratio of their corresponding sides are in proportion.

3. Similar is represented by a ~

4. 5:10 which is 1:2

5. 2:4 which is 1:2 Note: the ratio is the same for both height and width!

6. Therefore, the scale factor of Jim to Dave is 1:2

7. We can write Jim and Dave’s dimensions as proportions: 2 4 = 5 10

8. Similar Triangles:

9. How do you know if two triangles are similar? Just like with congruent triangles, we have a postulate and theorems to prove triangles are similar. They are: Angle-Angle Similarity Postulate (AA~) Side-Angle-Side Theorem (SAS~) Side-Side-Side Theorem (SSS~)

10. How do you know if two triangles are similar? http://www.mathopenref.com/similartriangles.html

11. Angle-Angle Similarity Postulate (AA~) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

12. Angle-Angle Similarity Postulate (AA~) More Examples:

13. Angle-Angle Similarity Postulate (AA~) More Examples:

14. Side-Angle-Side Similarity Theorem (SAS~) If an angle of one triangle is congruent to an angle of a second triangle and the sides including the angle are proportional, then the triangles are similar.

15. Side-Side-Side Similarity Theorem (SAS~) If the corresponding sides of two triangles are proportional, then the triangles are similar.