Geometry Sections 4.3 & 4.4 SSS / SAS / ASA

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Proving Triangles Congruent: SSS and SAS

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Presentation transcript:

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.

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.

is formed by the two sides. 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.

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.