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 ____ pairs of corresponding parts are congruent. The postulates introduced below allow us to

prove triangles congruent using only ____ pairs of corresponding parts.

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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 In a triangle, a side is included by two angles, if the side

is formed by the two sides.

is between the vertices of the two angles.

PEI

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.