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

______________ and all corresponding angles are

___________.

proportional

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

~ACE

AA

DCB

NONE

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~ABC

SSS

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AA

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