Quadrilaterals (NCERT Ch. 8)

• Prove properties of parallelograms: opposite sides parallel and equal, opposite angles equal.
• Use diagonals of parallelogram bisect each other.
• Identify special quadrilaterals: rectangle, rhombus, square, kite, trapezium.
• Apply mid-point theorem (intro) and symmetry arguments.

1. Parallelogram — Opposite sides parallel (definition) → opposite sides equal.
2. Opposite angles equal in parallelogram.
3. Diagonals bisect each other.
4. Rectangle — Parallelogram with one right angle → all angles 90°.
5. Rhombus — Parallelogram with adjacent sides equal → perpendicular diagonals.
6. Square — Both rectangle and rhombus.
7. Mid-point theorem (triangle) — Joining mid-points gives line parallel to base, half length.
8. NCERT proofs use triangle congruence from Chapter 7.

In parallelogram ABCD, show diagonals bisect each other.

Let diagonals meet at O. Prove △AOB ≅ △COD (ASA) → AO = CO, BO = DO.

• Skipping given-to-prove structure in geometry proofs.
• Using wrong congruence criterion (SSA is not valid).
• Forgetting units in length/angle statements.

• State one NCERT result from Quadrilaterals.
• Draw a neat diagram for a typical Quadrilaterals problem.

Open the Practice tab for graded questions on Quadrilaterals (NCERT Ch. 8).