Question

3 select the correct answer from each drop - down menu. if, then ( \triangle abc ) and ( \triangle efd ) are congruent by the asa criterion. if fd are congruent by the sas criterion. angle b is congruent to angle e angle c is congruent to angle e angle a is congruent to angle e

Explanation:

Step1: Recall ASA and SAS criteria

ASA (Angle - Side - Angle) criterion: Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
SAS (Side - Angle - Side) criterion: Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Step2: Analyze the triangles

In \(\triangle ABC\) and \(\triangle EFD\), we know \(AC = ED\) (marked as equal).
For ASA:
We need two angles. \(\angle C\) in \(\triangle ABC\) and \(\angle D\) in \(\triangle EFD\) (since \(AC = ED\) is the side). But if \(\angle A=\angle E\), we have \(AC = ED\) (side), \(\angle A=\angle E\) (angle) and \(\angle C=\angle D\) (from the figure's markings, assume the non - marked angles are related as per triangle congruence).
For SAS:
If \(\angle B=\angle E\), we have \(AC = ED\) (side), \(\angle B=\angle E\) (angle) and \(BC = FD\) (not given directly, but assume from the congruence logic).

Answer:

If \(\angle A\) is congruent to \(\angle E\), then \(\triangle ABC\) and \(\triangle EFD\) are congruent by the ASA criterion.
If \(\angle B\) is congruent to \(\angle E\), then \(\triangle ABC\) and \(\triangle EFD\) are congruent by the SAS criterion.