Question

select the correct answer from each drop - down menu.
if, then \\( \triangle abc \\) and \\( \triangle efd \\) are congruent by the asa criterion.
if, then \\( \triangle abc \\) and \\( \triangle efd \\) are congruent by the sas criterion.
reset next

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
From the figure, \(AC = DE\) (marked as equal). For \(\triangle ABC\) and \(\triangle EFD\) to be congruent by ASA, we need \(\angle A=\angle E\) and \(\angle C = \angle D\).

Step2: Recall SAS congruence criterion

SAS (Side - Angle - Side) criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
From the figure, \(AC = DE\). For \(\triangle ABC\) and \(\triangle EFD\) to be congruent by SAS, we need \(BC=FD\) and \(\angle C=\angle D\).

Answer:

If \(\angle A=\angle E\) and \(\angle C = \angle D\), then \(\triangle ABC\) and \(\triangle EFD\) are congruent by the ASA criterion.
If \(BC = FD\) and \(\angle C=\angle D\), then \(\triangle ABC\) and \(\triangle EFD\) are congruent by the SAS criterion.