1. 7-3 Triangle Similarity: AA, SSS, SAS
Geometry

2. Postulate 7-3-1 Angle – Angle (AA) Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
L Z Y X J K

3. Writing Proportionality Statements ∠A =∠D = 90°
Ex. 1 ) B
A C D E
a.).Explain why the triangles are similar.
b.) Write a similarity statement. ∟
1a) ∠BCA ≌∠ECD by vertical angles thm; AA
1b) ABC~DEC

4. THEOREM 7-3-2 Side-Side-Side (SSS) Similarity Theorem
If the three sides of one triangle are proportional to the 3 corresponding sides of another triangle, then the triangles are similar.
B C
E F
A D

5. THEOREM 7-3-3 Side-Angle-Side (SAS) Similarity Theorem
If two sides of one triangle are proportional to two sides of another triangle & their included angles are congruent, then the triangles are similar A D
B C
E F
∠B ≅∠E

6. Verifying Triangle Similarity2
° 1
Use Extra Example 2 picture. 3

7. Finding lengths in Similar Triangles
Ex. 3 Explain why & find CD. D E x
A B 3 C

8. Properties of Similarity
Reflexive Property of Similarity ~
Symmetric Property of Similarity
If ~ , then ~
Transitive Property of Similarity
If ~ & ~
then ~

9. Writing Proofs with Similarity Triangles
Ex. 4
Given: M is the midpoint of
N is the midpoint of ,
& P is the midpoint of
Prove:
(Hint: Use the Triangle Midsegment Theorem & SSS ). ~

10. Ex. 4 Proof Statements / Reasons

11. Assignment

12. Using Algebra
Ex. 3 – Use points G & J in the diagram below to find the slope of the line containing GJ. Name five other segments whose endpoints could be used to find the slope of the line.

13. Find the value of the variable
Ex. 4) Find y.
Use picture for #6 & 7

14. Generalization of Theorem 8.1
If two polygons are similar, then the ratio of any two corresponding lengths (such as altitudes, medians, angle bisector segments, and diagonals) is equal to the scale factor of the similar polygons.

15. Similar Triangles
Ex. 5) The segments in blue are special segments in the similar triangles. Find the value of the variable.
Use #45 as example

16. Slope
Slope formula
#29?