Question

select the correct answer from each drop - down menu. if, then △abc and △efd are congruent by the asa criterion. if, then △abc and △efd are congruent by the sas criterion.

Explanation:

Step1: Recall ASA criterion

The ASA (Angle - Side - Angle) criterion for triangle congruence states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent. In \(\triangle ABC\) and \(\triangle EFD\), if \(\angle A=\angle E\), \(AC = ED\) and \(\angle C=\angle D\), then \(\triangle ABC\cong\triangle EFD\) by ASA.

Step2: Recall SAS criterion

The SAS (Side - Angle - Side) criterion for triangle congruence states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. In \(\triangle ABC\) and \(\triangle EFD\), if \(AB = EF\), \(\angle B=\angle F\) and \(BC = FD\), then \(\triangle ABC\cong\triangle EFD\) by SAS.

Answer:

1. If \(\angle A=\angle E\), \(AC = ED\) and \(\angle C=\angle D\), then \(\triangle ABC\) and \(\triangle EFD\) are congruent by the ASA criterion.
2. If \(AB = EF\), \(\angle B=\angle F\) and \(BC = FD\), then \(\triangle ABC\) and \(\triangle EFD\) are congruent by the SAS criterion.