Question

based on the diagram, what additional information must be stated in order to prove △abd ≅ △dbc by the asa congruence theorem? (1 point) bc ≅ bc ∠a ≅ ∠d ac ≅ dc ab = bd

Explanation:

Step1: Recall ASA congruence theorem

The ASA (Angle - Side - Angle) congruence theorem 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 \(\triangle ABD\) and \(\triangle DBC\), we already know that \(\angle ABD=\angle DBC\) (the common - angle marked at \(B\)) and \(BD = BD\) (common side).

Step2: Identify the needed angle

We need to show that the other pair of angles are congruent. The angles adjacent to the common side \(BD\) are \(\angle A\) in \(\triangle ABD\) and \(\angle D\) in \(\triangle DBC\). So, we need \(\angle A\cong\angle D\).

Answer:

\(\angle A\cong\angle D\)