Question

5
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 criterion

ASA (Angle - Side - Angle) criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle ABC\) and \(\triangle EFD\), we know \(AC = ED\) (from the marks on the sides). For ASA, we need two angles. \(\angle C\) and \(\angle D\) are already marked as congruent (from the figure). If \(\angle B=\angle E\), then we have two angles (\(\angle B,\angle C\) in \(\triangle ABC\) and \(\angle E,\angle D\) in \(\triangle EFD\)) and the included side \(AC = ED\) (since \(AC\) is between \(\angle B\) and \(\angle C\) in \(\triangle ABC\) and \(ED\) is between \(\angle E\) and \(\angle D\) in \(\triangle EFD\)).

Step2: Recall SAS criterion

SAS (Side - Angle - Side) criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
We know \(AC = ED\). If \(\angle A=\angle E\), and assume \(AB = EF\) (not shown in the problem but for the sake of SAS, if we consider the side - angle - side structure where the angle is between the two sides). Here, if we take \(AC = ED\), \(\angle A=\angle E\) and \(AB = EF\) (by the problem's congruence logic for SAS), the triangles will be congruent by SAS.

Answer:

First blank: angle \(B\) is congruent to angle \(E\)
Second blank: angle \(A\) is congruent to angle \(E\)