Question

in the diagram, ( ac = ad ) and ( overline{ab} ) bisects ( angle a ). which congruence method is therefore used to conclude that ( \triangle abc cong \triangle adb )?

Explanation:

Step1: Analyze given information

We know \(AC = AD\) (side), \(\overline{AB}\) bisects \(\angle A\) so \(\angle CAB=\angle DAB\) (angle), and \(AB = AB\) (common side, side).

Step2: Recall congruence criteria

The \(SAS\) (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. Here, for \(\triangle ABC\) and \(\triangle ADB\), we have two sides (\(AC = AD\), \(AB=AB\)) and the included angle (\(\angle CAB=\angle DAB\)).

Answer:

D. SAS