1. **Problem statement:** Alva wants to prove that opposite sides in a parallelogram are congruent by establishing the congruence of a single pair of triangles. 2. **Given:** Quadrilateral ABCD with AB parallel to CD and AD parallel to BC. Diagonals AC and BD intersect at E. 3. **Goal:** Identify which pair of triangles Alva refers to and the congruence criterion to use. 4. **Key properties of parallelograms:** - Opposite sides are parallel and equal in length. - Diagonals bisect each other, so AE = EC and BE = ED. 5. **Triangles to consider:** Triangles ABE and CDE share the property that AE = EC and BE = ED because diagonals bisect each other. 6. **Congruence criterion:** To prove triangles congruent, use Side-Angle-Side (SAS) because: - AE = EC (side) - BE = ED (side) - Angle AEB = Angle CED (vertical angles, equal) 7. **Conclusion:** Alva is referring to triangles \(\triangle ABE\) and \(\triangle CDE\) and should use the side-angle-side (SAS) criterion. **Final answer:** Option D: \(\triangle ABE\) and \(\triangle CDE\) by side-angle-side