1. Class Greeting

2. Proving Similar Triangles
Chapter 7 – Lesson 3
Proving Similar Triangles

3. Objective: The students will be able to solve problems and prove triangles similar by using AA~.

4. There are several ways to prove certain triangles are similar
There are several ways to prove certain triangles are similar. AAS~, SSS~ and SAS~ are Similarity Theorems that will be used in proofs just as SSS, SAS, ASA, HL, and AAS were used to prove triangles congruent.

5. Example 1: Using the AA Similarity Postulate
Explain why the triangles are similar and write a similarity statement.
A  D
right angle theorem
BCA  DCE
vertical angle theorem

6. Answer: ∆ABE ~ ∆ACD by AA ~.
1. Explain why ∆ABE ~ ∆ACD.
A  A
Reflexive Property of 
ABE  C
right angle theorem
Answer: ∆ABE ~ ∆ACD by AA ~.
2. Find CD.
Answer: CD =

7. Example 2: Using the AA Similarity Postulate
ALGEBRA Given QT 2x 10, UT 10, find RQ and QT.
Alternate Interior Angles Theorem
by AA ~
definition of similar polygons
RQ = 5 + 3
Substitution
Substitution
RQ = 8
Simplify
Cross products
QT = 2(5) + 10
Substitution
Subtraction
QT = 20
Simplify
Division
Answer:
Example 3-2a

8. ALGEBRA Given and CE x + 2, find AC and CE.
Answer:
Example 3-2d

9. Kahoot!

10. Lesson Summary:
Objective: The students will be able to solve problems and prove triangles similar by using AA~.

11. Preview of the Next Lesson:
Objective: The students will be able to solve problems and prove triangles similar by using SSS~, and SAS~.

12. Stand Up Please