1. **Problem Statement:** Prove that each diagonal of a rectangle divides it into two congruent triangles. 2. **Recall the properties of a rectangle:** - Opposite sides are equal and parallel. - All angles are right angles ($90^\circ$). 3. **Consider rectangle $ABCD$ with diagonal $AC$:** - We want to prove that triangle $ABC$ is congruent to triangle $CDA$. 4. **Use the Side-Angle-Side (SAS) congruence rule:** - Side $AB = CD$ (opposite sides of rectangle). - Side $BC = DA$ (opposite sides of rectangle). - Angle $ABC = CDA = 90^\circ$ (all angles in rectangle). 5. **Check the diagonal $AC$ is common to both triangles:** - Side $AC$ is shared by triangles $ABC$ and $CDA$. 6. **Apply SAS:** - Triangles $ABC$ and $CDA$ have two sides and the included angle equal. - Therefore, $\triangle ABC \cong \triangle CDA$. 7. **Conclusion:** - Each diagonal divides the rectangle into two congruent triangles. $$\boxed{\triangle ABC \cong \triangle CDA}$$