Question

What additional information is needed in order to prove triangles CDE and CDQ congruent by ASA? (1 point) Responses ∠DCE≅∠DCQ angle upper D upper C upper E congruent to angle upper D upper C upper Q ∠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¯¯¯¯¯¯¯¯

Answer 1

To prove triangles CDE and CDQ congruent by the Angle-Side-Angle (ASA) postulate, we need to establish two angles and the side between them as congruent in each triangle.

The additional information needed is:

1. **One of the angles**: We already need \(\angle DCE \cong \angle DCQ\) or \(\angle E \cong \angle Q\).
2. **The sides**: We need to establish that \(DE \cong DQ\) or the other pairs of corresponding sides.

The most direct choice from your options for proving the triangles congruent by ASA would be:

- Either \(\angle DCE \cong \angle DCQ\) or \(\angle E \cong \angle Q\) (one angle from each triangle must be equal).
- Additionally, we should establish that either \(DE \cong DQ\) or the other sides of the triangles.

Thus, one possible complete response for the missing information could be:
- \(\angle DCE \cong \angle DCQ\) and \(DE \cong DQ\).

This gives us the necessary angles and the side to use ASA for proving the congruence of triangles CDE and CDQ.