1. Proving Triangles Similar
Lesson 5-3
Proving Triangles Similar
(AA, SSS, SAS)
Lesson 5-3: Proving Triangles Similar

2. AA Similarity (Angle-Angle)
If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar.
Given:
and
Conclusion:
Lesson 5-3: Proving Triangles Similar

3. SSS Similarity (Side-Side-Side)
If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. 5 11 22 8 16 10
Given:
Conclusion:
Lesson 5-3: Proving Triangles Similar

4. SAS Similarity (Side-Angle-Side)
If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle and the angles between them are congruent, then the triangles are similar. 5 11 22 10
Given:
Conclusion:
Lesson 5-3: Proving Triangles Similar

5. 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 …
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.
Lesson 5-3: Proving Triangles Similar

6. Lesson 5-3: Proving Triangles Similar
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
Lesson 5-3: Proving Triangles Similar

7. Lesson 5-3: Proving Triangles Similar
Problem #2
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
Step 5: Is there more?
Statements
Reasons
1. IJ = 3LN ; JK = 3NP ; IK = 3LP
Given
Division Property
Substitution
SSS Similarity
Lesson 5-3: Proving Triangles Similar

8. Lesson 5-3: Proving Triangles Similar
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?
Lesson 5-3: Proving Triangles Similar

9. Lesson 5-3: Proving Triangles Similar
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
Lesson 5-3: Proving Triangles Similar