Question

triangle congruence by sss and sas
guided practice
what additional information is needed to prove $\triangle abccong\triangle adc$ by the
sas postulate?
a. $angle cabcongangle cad$
b. $angle abccongangle adc$
c. $angle bcacongangle dca$

Explanation:

Step1: Recall SAS Postulate

SAS (Side - Angle - Side) 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 triangles

In \(\triangle ABC\) and \(\triangle ADC\), we can observe that \(AB = AD\) (marked as equal) and \(AC=AC\) (common side).

Step3: Determine the included angle

For SAS, the included angle between \(AB\) and \(AC\) in \(\triangle ABC\) is \(\angle CAB\), and the included angle between \(AD\) and \(AC\) in \(\triangle ADC\) is \(\angle CAD\).

Answer:

A. \(\angle CAB\cong\angle CAD\)