Question 2: Properties of Quadrilaterals & Congruence. Quadrilateral PQRS is a parallelogram with diagonal PR. 2.1 Write down two properties regarding the sides and diagonals of a parallelogram. (2) 2.2 Prove that PQR = RSP. Provide complete geometric reasons. (4)

Two properties regarding the sides and diagonals of a parallelogram are:

• Opposite sides are equal in length.
• Diagonals bisect each other.

To prove that $\triangle PQR \equiv \triangle RSP$, we can use the Side-Side-Side (SSS) congruence criterion.

Consider $\triangle PQR$ and $\triangle RSP$:

1. $PQ = SR$ (Opposite sides of a parallelogram are equal in length).
2. $QR = SP$ (Opposite sides of a parallelogram are equal in length).
3. $PR = RP$ (Common side to both triangles).

Therefore, by the SSS congruence criterion, we can conclude that: