Question

Question

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

(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 two triangles congruent using the Angle-Side-Angle (ASA) criterion, we need to establish that two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle.

In this case, you already have information about one angle congruence, specifically ∠E≅∠Q, which helps in establishing one of the angles for the ASA criterion.

To complete the congruence proof using ASA, you will need to provide one of the following pieces of information:

1. Another angle congruence: If you establish one more pair of congruent angles (for instance, ∠DCE≅∠DCQ), along with the included side (let's say DE≅DQ or CE≅CQ), you would have sufficient information to prove the triangles congruent.

2. Included side congruence: You could also provide that the sides DE and DQ are congruent, which would allow you to establish the ASA criterion with the given angle.

Given these considerations, the best option among your listed choices that would provide that needed additional angle congruence is:

∠DCE≅∠DCQ

This would give you two angles and the included side, thereby satisfying the ASA condition for triangle congruence.