Theorem 7-2 SSS Similarity Theorem If the sides of two triangles are in proportion, then the triangles are similar.
AB
BC AC
Given:
DE
EF DF
Prove: ABC ~ ADEF
=
=
А
-
De
X
Y
B
CE
F
Plan for Proof: Take X on DE so that DX = AB. Draw a line through X
DX XYDY.
parallel to EF. Then ADEF ~ ADXY and
With the given
DE EF “DF
proportion and DX = AB, you can deduce that AC = DY and BC = XY. Thus
AABC = ADXY by SSS. Therefore, AABC ~ ADXY, and AABC ~ ADEF
by the Transitive Property of Similarity.