1. The problem states that we have two right triangles sharing a vertical segment with points labeled D, C, E, A, and B, and right angles at D-C and A-B. 2. We are asked to identify the postulate that makes the triangles congruent from the options: SAS, ASA, Not Possible, AAS. 3. The given information includes that segment D is perpendicular to C, and A is perpendicular to B, indicating right angles. 4. Since both triangles share a vertical segment (common side), this side is congruent to itself by the Reflexive Property. 5. Each triangle has a right angle, so the angles at D-C and A-B are congruent (both 90 degrees). 6. If we know one more pair of corresponding sides or angles are congruent, we can use a postulate to prove congruence. 7. Given the right angle and the shared side, if the hypotenuses or another side are congruent, the SAS (Side-Angle-Side) postulate applies. 8. Therefore, the postulate that makes the triangles congruent is SAS. Final answer: SAS