Question

1. what other information is needed in order to prove

the triangles congruent using the sas congruence
postulate?
a. \\( \angle b a c \cong \angle d a c \\)
b. \\( \overline{a b} \parallel \overline{a d} \\)
c. \\( \overline{a c} \perp \overline{b d} \\)
d. \\( \overline{a c} \cong \overline{b d} \\)

Explanation:

Step1: Recall SAS Congruence Postulate

The SAS (Side - Angle - Side) Congruence Postulate 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.

Step2: Analyze the given information

We know that \(BC = CD\) (marked as equal in the figure). Also, \(AC\) is a common side. For SAS, we need the included angles. The included angle for \(\triangle ABC\) and \(\triangle ADC\) with respect to sides \(AB - AC\) and \(AD - AC\) (where \(BC = CD\)) is \(\angle BAC\) and \(\angle DAC\).

Answer:

A. \(\angle BAC\cong\angle DAC\)