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 which answer is correct and why

∠E≅∠Q
∠E≅∠Q

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

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

∠DCE≅∠DCQ
∠DCE≅∠DCQ
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Answer 1

To prove that the triangles are congruent using the Angle-Side-Angle (ASA) criterion, you need two angles and the included side congruent between the triangles.

Based on the options provided:

1. ∠E≅∠Q - This provides one pair of corresponding angles.
2. DE ≅ DQ - This provides one pair of congruent sides, but we need to ensure it is the side between the two angles.
3. CE ≅ CQ - This provides another pair of congruent sides, but if the included angles are not known, it wouldn't help with the ASA.
4. ∠DCE≅∠DCQ - This gives you the second pair of corresponding angles.

To apply ASA, you need two angles and the included side. If we assume that DE and DQ are the sides between ∠DCE and ∠E (or ∠Q), then having the information that ∠DCE≅∠DCQ is crucial.

Thus, the correct piece of information needed would be:

∠DCE ≅ ∠DCQ

This allows you to confirm that you have two angles (∠E and ∠DCE, and ∠Q and ∠DCQ) and the side DE ≅ DQ, fulfilling the ASA condition.