Geometry Section 4.4 cont. AAS. In the last section we learned of three triangle congruence postulates :. SSS SAS ASA. We also saw why SSA does not work as a congruence “shortcut”. Let’s look at some other possibilities.
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SSS SAS ASA
A counterexample demonstrates that AAA is not a valid test for congruence. Consider two equiangular triangles. What is true about the angles in each triangle? Are the triangles shown congruent?
They are all 60 degrees.
If we know the measures of two angles in a triangle, we will always be able to find the measure of the third angle.So, any time we have the AAS combination, we can change it into the ASA combination and the two triangles will then be congruent.
Theorem 4.5 AAS (Angle-Angle-Side) Congruence TheoremIf two angles and the non-included side of one triangle are congruent to the corresponding parts of anothertriangle, then the triangles are congruent.
Note: While ASA can be used anytime AAS can be used and vice-versa, they are different. The congruence markings on your triangles and the steps in your proof must agree with the congruence postulate/theorem you use.