1. **Problem Statement:** Given a parallelogram with its two diagonals intersecting, find the pairs of congruent triangles using the parallelogram side theorem and ASA (Angle-Side-Angle) congruence criterion. 2. **Recall the Parallelogram Side Theorem:** Opposite sides of a parallelogram are equal in length. 3. **Identify the triangles:** The diagonals intersect inside the parallelogram, creating four triangles. Label the parallelogram as ABCD with diagonals AC and BD intersecting at O. 4. **Apply the theorem:** Since ABCD is a parallelogram, AB = DC and AD = BC. 5. **Consider triangles AOB and COD:** - Side AO = CO (diagonals bisect each other) - Side BO = DO (diagonals bisect each other) - Angle AOB = Angle COD (vertically opposite angles) 6. **By ASA criterion:** Triangles AOB and COD are congruent. 7. **Similarly, consider triangles AOD and BOC:** - Side AO = CO (diagonals bisect each other) - Side DO = BO (diagonals bisect each other) - Angle AOD = Angle BOC (vertically opposite angles) 8. **By ASA criterion:** Triangles AOD and BOC are congruent. **Final answer:** The pairs of congruent triangles are $$\triangle AOB \cong \triangle COD$$ and $$\triangle AOD \cong \triangle BOC$$ by the parallelogram side theorem and ASA congruence.