1. Success Criteria LT: Today’s Agenda
Proportions
LT:
I will use ratio language to describe the relationship between two quantities
Do Now
Hand back test
Activity
HW#6
Success Criteria
Today’s Agenda
I can use ratio language to describe the relationship between two quantities

2. Hand out Activity
Today’s activity and accompanying worksheet will count as HW #36

3. Success Criteria LT: Today’s Agenda
Similar Triangles
LT:
I will use the criteria of similarity to determine if two shapes are similar
Do Now
Lesson
HW#7
Success Criteria
Today’s Agenda
I can use the criteria of similarity to determine if two shapes are similar

4. G.7 Proving Triangles Similar
(AA~, SSS~, SAS~)

5. 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 does not matter.

6. 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~

7. 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~

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

9. 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~

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

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

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

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

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

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

16. 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.

17. AA Problem #1 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
Step 5: Is there more?
Statements
Reasons C D E G F
Given
Alternate Interior <s
Alternate Interior <s
AA Similarity

18. SSS Problem #2 Step 1: Mark the given … and what it implies
Step 2: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Step 5: Is there more?
Statements
Reasons
1. IJ = 3LN ; JK = 3NP ; IK = 3LP
Given
Division Property
Substitution
SSS Similarity

19. SAS Problem #3 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………….
Step 5: Is there more?

20. 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

21. Similarity is reflexive, symmetric, and transitive.

22. Choose a Problem. Problem #1 AA Problem #2 SSS Problem #3 SAS
End Slide Show
Problem #1 AA
Problem #2
SSS
Problem #3
SAS

23. 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.