To determine the length of side \( a \), we need to use the information from the congruent triangles indicated by the AAS (Angle-Angle-Side) Congruence Theorem. Since the triangles are congruent, the corresponding sides are equal in length.
Typically, the AAS theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent, and thus all corresponding sides are equal.
If the left triangle has a known length for its side opposite to angle \( A \) (let's call it \( A \)), and we know that angle \( A \) is congruent to the angle in the right triangle, then side \( a \) in the right triangle must equal the length of the corresponding side from the left triangle.
Let’s label the known lengths from the left triangle and the angles properly, and use that to conclude the length of \( a \). Without those numeric values directly given here, I can't numerically state the length of \( a \), but based on the congruence established by AAS, we can state that:
According to the AAS Congruence Theorem, side \( a \) must be equal to the corresponding side in the left triangle.
If you currently have specific lengths provided for the left triangle, you can directly state the length of \( a \) based on that knowledge.
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