Question

mikal is proving that ( overline{ae} cong overline{ce} ).
which reason does the ( \bullet ) represent in mikals proof?
sas
sss
asa
aas

Explanation:

Step1: Recall triangle congruence theorems

• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.
• SSS (Side - Side - Side): All three sides of one triangle are congruent to all three sides of another triangle.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle.

Step2: Analyze the given information for \(\triangle ABE\) and \(\triangle CDE\)

• We know that \(\overline{AB}\cong\overline{CD}\) (given, a side).
• \(\angle ABE\cong\angle CDE\) (all right angles are congruent, an angle).
• \(\angle AEB\cong\angle CED\) (vertical angles theorem, an angle).
• The side \(\overline{AB}\) and \(\overline{CD}\) is not between the two angles \(\angle ABE\) and \(\angle AEB\) in \(\triangle ABE\), and \(\angle CDE\) and \(\angle CED\) in \(\triangle CDE\) respectively.

Answer:

AAS