Question

for each figure below, determine (by using the markings) if there is a pair of congruent triangles. if there is, name the congruence and give the property justifying the congruence.
note that the pairs of triangles are drawn as congruent, but you should not rely on how they are drawn in determining your answers.
if necessary, you may learn what the markings on a figure indicate.
(a)
(b)
select
△abc≅△□ by the
congruent:
not necessarily congruent

Explanation:

Step1: Identify the congruent parts

In \(\triangle ABC\) and \(\triangle DFE\), we have \(AC = DE\) (marked as equal), \(\angle A=\angle E\) (marked as equal), \(\angle C=\angle D\) (marked as equal).

Step2: Apply the congruence criterion

By the Angle - Side - Angle (ASA) congruence criterion. In ASA, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. Here, the side \(AC\) in \(\triangle ABC\) is between \(\angle A\) and \(\angle C\), and the side \(DE\) in \(\triangle DFE\) is between \(\angle E\) and \(\angle D\).

Answer:

Congruent: \(\triangle ABC\cong\triangle DFE\) by the ASA (Angle - Side - Angle) criterion.