1. Proving Triangles Similar
(AA~, SSS~, SAS~)

2. Similar Triangles
Two triangles are similar if they are the same shape. That means the vertices can be paired up so the angles are congruent. Size changes.

3. AA Similarity (Angle-Angle or AA~)
If 2 angles of one triangle are congruent to
2 angles of another triangle, then the triangles are similar.
Given:
and
Conclusion:
by AA~

4. SSS Similarity (Side-Side-Side or SSS~)
If the lengths of the corresponding sides of 2 triangles are proportional, then the triangles are similar.
Given:
Conclusion:
by SSS~

5. Example: SSS Similarity (Side-Side-Side)5 11 22 8 16 10
Given:
Conclusion:
By SSS ~

6. SAS Similarity (Side-Angle-Side or SAS~)
If the lengths of 2 sides of a triangle are proportional to the lengths of 2 corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.
Given:
Conclusion:
by SAS~

7. Example: SAS Similarity (Side-Angle-Side)5 11 22 10
Conclusion:
Given:
By SAS ~

8. #1 A 80 D E 80 B C ABC ~ ADE by AA ~ Postulate 11111111#11# 1
#11# 1  A #1
80 D E
80 B C
ABC ~ ADE by AA ~ Postulate
Slide from MVHS

9. C #2 6 10 D E 5 3 A B
CDE~ CAB by SAS ~ Theorem
Slide from MVHS

10. L #3 5 3 M 6 6 K N 6 10 O
KLM~ KON by SSS ~ Theorem
Slide from MVHS

11. A 20 #4 D 30 24 16 B C 36
ACB~ DCA by SSS ~ Theorem
Slide from MVHS

12. L #5 15 P A 25 9 N
LNP~ ANL by SAS ~ Theorem
Slide from MVHS

13. Similarity is reflexive, symmetric, and transitive.
Proving Triangles Similar
Similarity is reflexive, symmetric, and transitive.
Steps for proving triangles similar:
1. Mark the Given.
2. Mark …
Reflexive (shared) Angles or Vertical Angles
3. Choose a Method. (AA~, SSS~, SAS~)
Think about what you need for the chosen method and be sure to include those parts in the proof.

14. AA Problem #1 Step 1: Mark the given … and what it implies
Step 1: Mark the given … and what it implies
Step 2: Mark the vertical angles AA
Step 3: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Statements
Reasons 4. C D E G F
Given
Alternate Interior <s
Alternate Interior <s
AA Similarity

15. SSS Problem #2 Step 1: Mark the given … and what it implies
Step 1: Mark the given … and what it implies
SSS
Step 2: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Statements
Reasons
Given
Substitution
SSS Similarity

16. SAS Problem #3 Step 1: Mark the given … and what it implies
Step 1: Mark the given … and what it implies
Step 2: Mark the reflexive angles
SAS
Step 3: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Next Slide………….

17. Statements
Reasons
G is the Midpoint of
H is the Midpoint of
Given
2. EG = DG and EH = HF
Def. of Midpoint
3. ED = EG + GD and EF = EH + HF
Segment Addition Post.
4. ED = 2 EG and EF = 2 EH
Substitution
Division Property
Reflexive Property
SAS Postulate

18. The End 1. Mark the Given. 2. Mark … Shared Angles or Vertical Angles
3. Choose a Method. (AA, SSS , SAS)
**Think about what you need
for the chosen method and
be sure to include
those parts in the proof.
The End