Two triangles are next to each other: the sides and angles of the left triangle have numerical values, and the sides of the right triangle are labeled a, b, and c. Tick marks and arcs are used to show congruent sides and angles of the triangles.

Question

Two triangles are next to each other: the sides and angles of the left triangle have numerical values, and the sides of the right triangle are labeled a, b, and c. Tick marks and arcs are used to show congruent sides and angles of the triangles.
These triangles are congruent by the AAS Congruence Theorem. What is the length of a?

(1 point)
According to the AAS Congruence Theorem, side a must be 
.

GPT-4o mini · Answer

To determine the length of side $ a $ in the right triangle, we need specific numerical values for the sides and angles of the left triangle, which would reveal the corresponding congruent parts in the right triangle. Since you mention the AAS (Angle-Angle-Side) Congruence Theorem, it indicates that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the two triangles are congruent. This means that all corresponding sides of the triangles are also equal. If we had the measures of the angles and the lengths of the corresponding sides in the left triangle, we would set side $ a $ equal to the corresponding side in the left triangle. If you can provide the specific lengths and angles from the left triangle, I can help you determine the length of side $ a $.