Question

if you wanted to explain why △abd≅cbd by the sas congruence theorem, which of the following would be helpful to know? (1 point)
bd is the angle bisector of ∠abc.
bd is the angle bisector of ∠bcd.
ac is the angle bisector of ∠bcd.
ac is the angle bisector of ∠bad.

Explanation:

The SAS (Side - Angle - Side) Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In \(\triangle ABD\) and \(\triangle CBD\), side \(BD\) is common. To use SAS to prove \(\triangle ABD\cong\triangle CBD\), we need to know that the angles formed by the common side \(BD\) and the other two sides in each triangle are equal. If \(BD\) is the angle - bisector of \(\angle ABC\), then \(\angle ABD=\angle CBD\). Also, we assume there are equal side - lengths (not mentioned in the problem but required for SAS). This angle - equality condition helps in applying the SAS theorem.

Answer:

\(\overline{BD}\) is the angle bisector of \(\angle ABC\).