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

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

∠DCE≅∠DCQ
∠DCE≅∠DCQ

DE¯¯¯¯¯¯¯¯ ≅ DQ¯¯¯¯¯¯¯¯
DE¯¯¯¯¯¯¯¯ ≅ DQ¯¯¯¯¯¯¯¯
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Answer 1

To use the Angle-Side-Angle (ASA) congruence rule to prove the triangles congruent, you need to know two angles and the included side between those angles.

In the context provided, if you already have the angle \( \angle DCE \) and the side \( CE \) compared to \( \angle DCQ \) and the side \( CQ \), you would need the measure of the angle that corresponds to those sides to establish the third angle.

Thus, you need the information that either:

Option: \(\angle E \cong \angle Q\)

This additional information would ensure that two angles and the included side (the shared side \( DC \)) is known, allowing you to prove that the triangles are congruent by ASA.