Triangle Similarity

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.

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

SSS~AB BC AC

A’B’ B’C’ A’C’You should be able

to identify a scale factor.

A

B C

A’

B’ C’

915

12

4.5 7.5

6

==

9 12 15

4.5 6 7.5 ==

Scale factor is 2 to 1or 1/2

SAS~ The included angles are the angles that are formed by the two pairs of corresponding sides.

A

65 C

A’

65 C’

9

12

4.5

6

POSTULATESAA~SSS~SAS~

A Postulate is a statement that is accepted to be true without PROOF.

What did you discover with your triangle cutting exercise?

TC

A

Do NOT cut thisoriginal Triangle.

(cut parallel to C’T’)

T’C’

A’

T’’’C’’’

A’’’

T’’C’’

A’’

Hopefully…

Corresponding angles are Corresponding sides are proportional

Regardless of where you make your cut.

Side-Splitting Theorem

A line parallel to one side of a triangle divides the other two sides proportionally.

3 4

8 10 2/3

How many ratios do you see?

3 4

8 10 2/3

How many ratios do you see?

3 4

8 10 2/3

3 8 11

4 10 2/3 14 2/3= =