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)

Step 1: Answer question 2.1. Two properties regarding the sides and diagonals of a parallelogram are: • Opposite sides are equal in length. • Diagonals bisect each other.

Step 2: Prove congruence for question 2.2. 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: $\boxed{\triangle PQR \equiv \triangle RSP}$

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