Geometry 6.5SWLT: Use the SSS & SAS Similarity Theorems

Side-Side-Side (SSS) Similarity Theorem

If the corresponding side lengths of two triangles are proportional, then the triangles are similar.

, then ABC RST

A

B C

R

S T

Using the SSS Theorem

Which is Similar to ABC?

A

B C

8 9

12

D

E F4 6

8

G

J H24

18 16

Compare the Triangles by finding the ratios of the corresponding Sides

ABC DEF? Shortest Sides

Longest Sides

Remaining Sides

The ratios are not the same, so ABC is not similar to DEF

ABC GHJ? Shortest Sides

Longest Sides

Remaining Sides

All ratios are equal, ABC GHJ

Side-Angle-Side (SAS) Similarity Theorem

If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides that form these angles are proportional, then the triangles are similar

If and ,

then XYZ MNP

X

Z

Y

M

P

N

Using SAS… is PRQ TSR? PRQ and SRT are vertical

angles, are congruent

Find the Ratios of the corresponding sides Shorter Sides

Longer Sides

The corresponding sides proportional, so PRQ TRS

R

P

Q

S

T

18

24

12

9