Download Honors Geometry Section 8.3 Similarity Postulates and Theorems

Honors Geometry Section 8.3
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
___________.
Therefore, in order to say that two
triangles are similar by the definition
of similarity, we would need to know
that all three sides of one triangle are
proportional to the corresponding
sides of the second triangle and that
all three angles of the first triangle are
congruent to the corresponding angles
in the second triangle.
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.
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