1. Section 8.3 Proving Triangles Similar
By: Asad Ashraf

2. What is Similarity
Similar figures are figures in which the shape is exactly the same, but the size is not.
A Dilation is an enlargement of a figure. It is still similar, however.
A Reduction is a reduction of a figure. This is also similar.
**Remember that similar figures are not necessarily congruent**

3. Proving Triangles Similar
There are several methods to prove triangles similar.
These are very similar to the methods of proving triangles congruent.
The methods are AAA~, AA~, SAS~, and SSS~.

4. AAA~ Postulate
AAA~  Postulate  - If three angles of one triangle are congruent to three angles of a 2nd triangle then the triangles are similar.

5. AA~ Theorem
AA~ if 2 angles of one triangle are congruent to two angles of a 2nd triangle then the triangles are similar.
This is proved by the No-Choice Theorem and AAA~ Theorem combined.

6. SSS~ Theorem
SSS~ If 3 sides of one triangle are proportional to three sides of a 2nd triangle then the two triangles are similar.

7. SAS~ Theorem
SAS ~  If two sides of one triangle are proportional to the corresponding two sides of a 2nd triangle and their included angles are congruent, then the triangles are similar.

8. Sample Problems
Click Here
SSS~ and SAS~ Problems

9. Sample Problems Are these triangles ~? Answer: Yes they are because
Included angles were given congruent and the ratios of the sides are congruent as well.

10. Practice Problems
Prove that an acute angle of one right angle is congruent to the vertex angle of an isosceles triangle, they are similar.
Always, Sometimes, Never
If 2 triangles are similar, they are congruent ____
If 2 triangles are congruent, they are similar ____
2 rectangles are similar if neither is a square ____
2 right triangles are similar____
Answers: A, S, S, S

11. Practice Problems
Are any 2 isosceles triangles similar? Show all work.

12. Practice Problems Are these triangles similar? Why or why not?
Answer: NO

13. Practice Problems Given: XS and RY are Altitudes of RTS
Prove: Triangle TSX is similar to Triangle TYR

14. Works Cited
Our Book
“Similar Triangles”. Mathwarehouse.com. May 27,2008.<
“Chapter 8”. Teacherweb.org May 27,2008.<