In order to prove the triangles pictured below congruent using ASA, what is the one piece of additional information that is needed?

Question

(1 point)
Responses

∠E≅∠Q
∠E≅∠Q

DE¯¯¯¯¯¯¯¯ ≅ DQ¯¯¯¯¯¯¯¯
DE¯¯¯¯¯¯¯¯ ≅ DQ¯¯¯¯¯¯¯¯

CE¯¯¯¯¯¯¯¯ ≅ CQ¯¯¯¯¯¯¯¯
CE¯¯¯¯¯¯¯¯ ≅ CQ¯¯¯¯¯¯¯¯

∠DCE≅∠DCQ

Answer 1

To prove two triangles congruent using the Angle-Side-Angle (ASA) theorem, you need two angles and the included side between them to be congruent in both triangles.

If you already have the angles (∠E ≅ ∠Q) and a side (DE ≅ DQ), the one additional piece of information needed to satisfy ASA is that the angles adjacent to the included sides are also congruent.

In this case, the best choice from the options given is:

∠DCE ≅ ∠DCQ

This provides the second angle needed to establish congruence via ASA.