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) o $overline{ac}$ is the angle bisector of ∠bad. o $overline{bd}$ is the angle bisector of ∠bcd o $overline{ac}$ is the angle bisector of ∠bcd o $overline{bd}$ is the angle bisector of ∠abc.

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. For \(\triangle ABD\) and \(\triangle CBD\), if \(BD\) is the angle - bisector of \(\angle ABC\), then \(\angle ABD=\angle CBD\). Also, \(BD = BD\) (common side). If we can show that \(AB = CB\) (another pair of sides), we can use SAS. Knowing that \(BD\) is the angle - bisector of \(\angle ABC\) gives us the included angle part for the SAS theorem.

Answer:

BD is the angle bisector of ∠ABC.