If angle A and angle C are right angles and AD is congruent to BC, what postulate or theorem justifies the congruence statement triangle BCD congruent to triangle DAB?
The two triangles have the same hypotenuse (BD). AD is a leg of triangle DAB and BC is a leg of triangle BCD. So, the triangles have a leg that is congruent and hypotenuses that are also congruent. The HL (Hypotenuse Leg) postulate that states if there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent justifies that the two triangles are congruent.