Download Honors Geometry Section 4.2 SSS / SAS / ASA

Geometry Sections 4.3 & 4.4
SSS / SAS / ASA
To show that two triangles are congruent
using the definition of congruent polygons,
as we did in the proof at the end of section
4.1, we need to show that all ____
6 pairs of
corresponding parts are congruent. The
postulates introduced below allow us to
prove triangles congruent using only ____
3
pairs of corresponding parts.
Postulate 19: SSS (Side-Side-Side) Postulate
If 3 sides of one triangle are
congruent to 3 sides
of a second triangle, then the
triangles are congruent.
We need to consider the following definitions to help
us understand the next two postulates.
In a triangle, an angle is included by two sides, if
the angle is formed by the two sides.
In a triangle, a side is included by two angles, if
the side is between the vertices of the two angles.
PE
I
Postulate 20: SAS (Side-Angle-Side) Postulate
If two sides and the included angle
of one triangle are congruent to two
sides and the included angle of a
second triangle, then the triangles are
congruent.
Why does the angle have to be the included
angle? Why can’t we have ASS? Well, other
than the fact that it is a bad word, ASS doesn’t
always work to give us congruent triangles.
Consider the following counterexample.
Postulate 21: ASA (Angle-Side-Angle) Postulate
If two angles and the included side of
one triangle are congruent to two angles
and the included side of a second triangle,
then the triangles are congruent.
Example 3: Determine whether
each pair of triangles can be
proven congruent by using the
congruence postulates. If so, write
a congruence statement and
identify the postulate used. None
is a possible answer.