Question

what additional information is needed in order to prove triangles cde and cdq congruent by asa? (1 point) ∠e ≅ ∠q ∠dce ≅ ∠dcq overline{de} ≅ overline{dq} overline{ce} ≅ overline{cq}

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle CDE\) and \(\triangle CDQ\), we already have \(CD = CD\) (common side). We also have one pair of angles (\(\angle CDE=\angle CDQ\) as given by the equal - arc - like markings).

Step2: Identify the missing angle

The included side is \(CD\). For ASA, we need another pair of angles. The angles adjacent to the side \(CD\) are \(\angle DCE\) and \(\angle DCQ\). If \(\angle DCE\cong\angle DCQ\), then in \(\triangle CDE\) and \(\triangle CDQ\), we have \(\angle DCE\cong\angle DCQ\), \(CD = CD\), and \(\angle CDE=\angle CDQ\) (by the given angle markings).

Answer:

\(\angle DCE\cong\angle DCQ\)