4-3 Triangle Congruence by ASA and AAS

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Presentation transcript:

4-3 Triangle Congruence by ASA and AAS

Angle-Side-Angle Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Using ASA Which two triangles are congruent by ASA?

Writing a Proof Using ASA

Angle-Angle-Side Theorem If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.

Writing a Proof Using AAS

Determining Whether Triangles Are Congruent  Are the triangles congruent?

Is There “Angle-Side-Side” Congruence? Absolutely…NOT! If we are given two sides and an angle that is NOT their included angle, there are three possibilities: the included angle could be acute, right, or obtuse which affects the length of the third side. Since we have “options”, there is no guarantee that both triangles have the same third side. *You can remember that this is “bad” because the abbreviation is a bad word! 