Question

based on the information marked in the diagram, △abc and △def must be congruent.
a. true
b. false

Explanation:

Step1: Identify congruence criteria

In right - angled triangles $\triangle ABC$ and $\triangle DEF$, we see that one leg is marked equal (the short legs $AC = DF$) and the right - angles $\angle C=\angle F = 90^{\circ}$. Also, the hypotenuses are not marked equal, but by the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles, if the hypotenuse and one leg of a right - angled triangle are congruent to the hypotenuse and one leg of another right - angled triangle, the triangles are congruent. Here, since the right - angles are equal and one leg is equal, and we assume the triangles are right - angled, we can also use the Side - Angle - Side (SAS) congruence criterion as we have a side ($AC = DF$), the included right - angle, and the other side (the vertical sides which are part of the right - angle) is implicitly determined by the right - angle and the given side.

Step2: Determine congruence

Based on the above - mentioned congruence criteria, $\triangle ABC\cong\triangle DEF$.

Answer:

A. True