Level 1: Core concepts Check (Aiming for a Pass - 'S')

1. Define: What is a parallelogram?

2. List: State the four main properties of a parallelogram concerning its sides, angles, and diagonals.

3. Identify: State the four conditions under which a quadrilateral can be proven to be a parallelogram.

4. Recall: What property makes a parallelogram a rectangle?

5. Recall: What property makes a parallelogram a rhombus?

Level 2: Connecting the Dots (Aiming for a Credit - 'C'/'B')

1. Explain: A student claims a quadrilateral is a parallelogram because its diagonals are equal. Is this sufficient? If not, what shape could it be, and what additional condition is needed for it to be a parallelogram?

2. Apply (Proof): In parallelogram ABCD, the midpoint of side BC is E. The line segment DE is extended to meet the line AB extended at Q. Prove that AB = BQ.

3. Problem-Solve: ABCD is a rhombus. If the diagonal AC = 16 cm and the diagonal BD = 12 cm, find the perimeter of the rhombus. (Hint: What is the property of the diagonals of a rhombus?).

Level 3: Exam Challenge (Aiming for a Distinction - 'A')

Proof Analysis: In parallelogram ABCD, the midpoints of the sides AB, BC, CD, and AD are P, Q, R, and S respectively.

(a) Prove that △APS≡△CRQ.

(b) Hence, prove that PQRS is a parallelogram.