Question

32 suppose ( overline{ab} cong overline{ae} ). can you use the sss postulate or the sas postulate to prove ( \triangle abc cong \triangle aed )? by sss only both apply neither apply by sas only

Explanation:

Step1: Analyze the SSS (Side - Side - Side) Postulate

The SSS postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
From the figure, we have \(AB = AE\) (given), \(BC=ED\) (marked with two - tick marks), and \(AC = AD\) (marked with one - tick mark). So, by SSS (\(\triangle ABC\) and \(\triangle AED\) have \(AB\cong AE\), \(BC\cong ED\), \(AC\cong AD\)), \(\triangle ABC\cong\triangle AED\) by SSS.

Step2: Analyze the SAS (Side - Angle - Side) Postulate

The SAS 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.
The included angle for \(\triangle ABC\) is \(\angle BAC\) and for \(\triangle AED\) is \(\angle EAD\). Since \(AB = AE\), \(AC = AD\), and \(\angle BAC=\angle EAD\) (the non - ticked angles between the sides \(AB - AC\) and \(AE - AD\) respectively), \(\triangle ABC\cong\triangle AED\) by SAS.

Answer:

both apply