Comment by desertrider12

We know angle EBD equals BAC, since the sum of triangle ABC's interior angles is 180 degrees and the sum of the 3 angles at B are also 180 degrees. We also know angle DEB is 90 degrees since DE was constructed to be perpendicular to CB. Finally, D was placed at a distance c from B. The two triangles have the same angles and the same side lengths opposite the right angles, so they must be congruent.