Question

1. in the diagram, (overline{bd}) bisects (angle abc). what additional congruence must be established to prove (\triangle adbcong\triangle cdb) by sas?

side pair:
angle pair:
side pair:

Explanation:

Step1: Analyze the given information

Since \(BD\) bisects \(\angle ABC\), we have \(\angle ABD=\angle CBD\). Also, \(BD = BD\) (common side).

Step2: Recall the SAS (Side - Angle - Side) criterion

For \(\triangle ADB\cong\triangle CDB\) by SAS, we need two sides and the included angle to be congruent. We already have \(\angle ABD=\angle CBD\) (angle) and \(BD = BD\) (side).

Step3: Determine the additional side

The additional side pair should be \(AB = CB\).

Answer:

Side Pair: \(AB = CB\), Angle Pair: \(\angle ABD=\angle CBD\), Side Pair: \(BD = BD\)