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BOTH the triangles share the side [tex]\overline {\text{AC}}[/tex], EQUAL pairs of congruent side. The given congruent angles are included angles, so ΔABC is CONGRUENT to ΔCDA by SAS Congruency rule.
Three corresponding parts must be equal in order to demonstrate the congruence of two triangles.
The first two postulates—Side-Angle-Side (SAS) and Side-Side-Side (SSS)—concentrate primarily on the side aspects, whereas the following lesson discusses two other postulates that do the opposite. The Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates describe these relationships.
The two triangles are congruent if we can prove that two sides and the included angle of one triangle are congruent with two sides and the included angle of another triangle.
The Side Angle Side Postulate, or SAS, is the theory behind this. The Side-Angle-Side Postulate also allows us to demonstrate that triangle ABC and triangle EDC are congruent.
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