BE is a common side for both triangles and
Since we have
Therefore, is an isosceles triangle.
Thus, is congruent to (RHS)
Thus DT//BA (alt. angles)
By Pythagoras’ Theorem, we have
Hence and are congruent (SSS).
Thus DB//TA (alt. angles)
Therefore, ABDT is a parallelogram since it has two pairs of parallel sides.