1. Triangle Similarity

2. Two Triangles are similar if :
AA ~ : two pairs of corresponding angles are congruent,
SSS~ : all three pairs of corresponding sides are proportional, or
SAS~ : two pairs of corresponding sides are proportional and their included angles are congruent.

3. AA ~
If 2 corresponding angles are congruent then the 3rd pair of corresponding angles must be congruent also.
(Angle sum of a triangle = 180°.) A
65°
49° A’
65°
49°

4. SSS~ = = AB BC AC A’B’ B’C’ A’C’
You should be able to identify a scale factor. = = A B C 15 9 12 A’ =
7.5
4.5 B’ C’
Scale factor is 2 to 1
or 1/2 6

5. SAS~
The included angles are the angles that are formed by the two pairs of corresponding sides. A
65° C 9 12 A’
4.5
65° C’ 6

6. A Postulate is a statement that is accepted to be true without PROOF.
POSTULATES
AA~
SSS~
SAS~
A Postulate is a statement that is accepted to be true without PROOF.

7. What did you discover with your triangle cutting exercise?
(cut parallel to C’T’) T C A
Do NOT cut this
original Triangle. A’ C’ T’
T’’’
C’’’
A’’’
A’’
C’’
T’’

8. Hopefully… Corresponding angles are @
Corresponding sides are proportional
Regardless of where you make your cut.

9. Side-Splitting Theorem
A line parallel to one side of a triangle divides the other two sides proportionally. 4 3 8
10 2/3

10. How many ratios do you see?4 3 8
10 2/3

11. How many ratios do you see?4 3 8
10 2/3
/ /3 = =