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Question

Two triangles have a common adjacent side and congruent angles.

What additional information is needed in order to prove triangles CDE and CDQ congruent by ASA?

(1 point)
Responses

∠E≅∠Q
angle upper E congruent to angle upper Q

DE¯¯¯¯¯¯¯¯≅DQ¯¯¯¯¯¯¯¯
Modifying above upper D upper E with bar congruent to Modifying above upper D upper Q with bar

CE¯¯¯¯¯¯¯¯≅CQ¯¯¯¯¯¯¯¯
Modifying above upper C upper E with bar congruent to Modifying above upper C upper Q with bar

∠DCE≅∠DCQ
angle upper D upper C upper E congruent to angle upper D upper C upper Q
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Answer 1

To prove triangles CDE and CDQ congruent by ASA (Angle-Side-Angle), you need to ensure that you have two angles and the included side that are congruent. Given that the triangles already have a common adjacent side (CD) and congruent angles (let's refer to them as ∠CDE and ∠CDQ), you need to establish the congruence of one additional angle or side.

Among the options provided, the additional information needed is:

∠E≅∠Q

This means that angle E must be congruent to angle Q. With this information, you will have two angles (∠CDE and ∠E≅∠Q) and the included side (CD), which are sufficient to prove the triangles CDE and CDQ congruent by ASA.