Question

is \\( \triangle a b c \cong \triangle d f e \\) ? explain.

Explanation:

Step1: Identify the given information

We have two right - angled triangles \(\triangle ABC\) and \(\triangle DFE\). \(\angle C=\angle E = 90^{\circ}\), \(BC = FE\) (marked as equal), \(\angle B=\angle F\) (given by the angle markings).

Step2: Recall the ASA (Angle - Side - Angle) congruence criterion

The ASA congruence 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.
In \(\triangle ABC\) and \(\triangle DFE\), \(\angle C=\angle E\), \(BC = FE\), \(\angle B=\angle F\). The side \(BC\) is between \(\angle B\) and \(\angle C\) in \(\triangle ABC\), and the side \(FE\) is between \(\angle F\) and \(\angle E\) in \(\triangle DFE\).

Answer:

Yes, the triangles are congruent by ASA.