Download Honors Geometry Section 8.3 Similarity Postulates and Theorems

Geometry Sections 8.4 & 8.5
Similarity Postulates and Theorems
To say that two polygons are
similar by the definition of
similarity, we would need to know
that all corresponding sides are
proportional and all
______________
corresponding angles are
congruent
___________.
The following postulate and
theorems give us easier methods
for determining if two triangles are
similar.
Angle-Angle Similarity Postulate
(AA Similarity)
If TWO ANGLES OF ONE TRIANGLE
ARE CONGRUENT TO TWO ANGLES
OF A SECOND TRIANGLE, then the
triangles are similar.
Side-Angle-Side Similarity
Theorem (SAS Similarity)
If TWO SIDES of one triangle are
PROPORTIONAL to TWO SIDES of a
second triangle and the INCLUDED
ANGLES are CONGRUENT, then the
triangles are similar.
An included angle of two sides is
the angle FORMED BY THOSE TWO
SIDES.
Side-Side-Side Similarity Theorem
(SSS Similarity)
If the THREE SIDES of one triangle
are PROPORTIONAL to the THREE
SIDES of a second triangle, then
the triangles are similar.
Examples: Determine if the
triangles are similar. If so, write a
similarity statement
and
identify the postulate or theorem
used.
A
B
C
D
E
AA
ACE ~ DCB
NONE
31.25
20

?
25
16
? 18.75

12
1.5625  1.5625  1.5625
SSS
ABC ~ FDE
AA
ABC ~ EDC