1. The problem asks to identify the postulate that makes the triangles congruent given a right triangle with points D, C, A, B and a segment E perpendicular between A and B. 2. The common triangle congruence postulates are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and sometimes Not Possible if no postulate applies. 3. Since the triangle has right angles at C and A, and segment E is perpendicular between A and B, we have right angles and a shared side or segment. 4. The right angle at C and the right angle at A provide two angles. 5. If the segment E is shared or equal in both triangles, and one side adjacent to the right angle is equal, then the SAS postulate applies. 6. Therefore, the triangles are congruent by SAS (Side-Angle-Side) postulate because we have a side, the included right angle, and another side equal. Final answer: SAS