1. **Problem Statement:** Prove that the diagonals of a rectangle are equal. 2. **Given:** Rectangle ABCD with diagonals AC and BD intersecting at point O. 3. **Properties of a rectangle:** Opposite sides are equal: $AB = DC$ and $AD = BC$. 4. **Angles:** Each angle in a rectangle is $90^\circ$, so $\angle A = \angle C = 90^\circ$. 5. **Triangles to consider:** Triangles $\triangle ABC$ and $\triangle CDA$. 6. **Congruence criteria (SAS):** Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding parts of the other triangle. 7. **Apply SAS:** - Side $AB = DC$ (opposite sides of rectangle) - Side $AD = BC$ (opposite sides) - Angle $\angle A = \angle C = 90^\circ$ Therefore, $\triangle ABC \cong \triangle CDA$ by SAS. 8. **Conclusion:** Corresponding parts of congruent triangles are equal, so $AC = BD$. **Final answer:** The diagonals $AC$ and $BD$ of rectangle $ABCD$ are equal in length.