1. **State the problem:** Given an isosceles trapezoid ROMA, prove that the diagonals $\overline{RM}$ and $\overline{AO}$ are congruent. 2. **Given:** ROMA is an isosceles trapezoid. 3. **To prove:** $\overline{RM} \cong \overline{AO}$. 4. **Proof steps:** - Step 1: Given. - Step 2: $\overline{OR} \cong \overline{MA}$ because in an isosceles trapezoid, the legs are congruent. - Step 3: $\angle ROM \cong \angle AMO$ because the base angles of an isosceles trapezoid are congruent. - Step 4: $\overline{OM} \cong \overline{MO}$ is true by the Reflexive Property (a segment is congruent to itself). - Step 5: By the SAS (Side-Angle-Side) Congruence Postulate, triangles $\triangle ROM$ and $\triangle AMO$ are congruent. - Step 6: Therefore, corresponding parts of congruent triangles are congruent, so $\overline{RM} \cong \overline{AO}$. 5. **Summary:** We used properties of isosceles trapezoids and triangle congruence postulates to prove the diagonals are congruent.