Question

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 Postulate

SSS (Side - Side - Side) Postulate requires three pairs of corresponding sides to be congruent. From the figure, we know \(AB\cong AE\) (given), but we cannot confirm that \(BC\cong ED\) and \(AC\cong AD\) just from the information provided for the SSS condition.

Step2: Analyze the SAS Postulate

SAS (Side - Angle - Side) Postulate requires two pairs of corresponding sides and the included angle to be congruent. We have \(AB\cong AE\) (given). Also, from the markings in the figure, we can see that the angles between the sides: \(\angle BAC\) and \(\angle EAD\) (the non - marked angles adjacent to the given equal sides). Since \(AB\cong AE\), and the sides adjacent to the angles (the sides with one mark) are congruent (\(AC\) and \(AD\) are marked as equal), and we can calculate the included angles.
The angle adjacent to \(60^{\circ}\) in \(\triangle ABC\) (the included angle) and the angle adjacent to \(120^{\circ}\) in \(\triangle AED\) (the included angle) can be found. The angle in \(\triangle ABC\) (let's call it \(\angle BAC\)): if we consider the linear pair with \(60^{\circ}\) (not relevant for the included angle in SAS as we use the non - linear pair angles related to the congruent sides). In fact, from the side markings (the sides with one cross), \(AC = AD\), \(AB=AE\), and the angles between them (by angle subtraction from the known angles in the figure, we can get that the included angles are equal).

Answer:

by SAS only