Yes, the two triangles are congruent. We can write the congruence statement as follows: $\triangle ABC ≅ \triangle FED$
Work Step by Step
In these triangles, $\angle B$ and $\angle C$ are both right angles, $BC$ and $EF$ are both $6$, and the hypotenuses $AC$ and $FD$ are both $10$. This means that $\triangle ABC ≅ \triangle FED$ because of the hypotenuse-leg theorem, which states that if one leg and the hypotenuse of a right triangle are congruent to one leg and the hypotenuse of another right triangle, then the triangles are congruent.