Quadrilaterals Class 9 Notes: Properties, Parallelogram Theorems and Mid-Point Theorem

Quick answer: Quadrilaterals is a 5–6 mark chapter where the mid-point theorem and ‘prove it is a parallelogram’ questions repeat every year.

Angle sum

Sum of angles of a quadrilateral = 360°. Example: angles in ratio 3 : 5 : 9 : 13 → 30x = 360 → 36°, 60°, 108°, 156°.

Properties table

Shape	Sides	Angles	Diagonals
Parallelogram	Opposite equal & parallel	Opposite equal	Bisect each other
Rectangle	Opposite equal	All 90°	Equal, bisect
Rhombus	All equal	Opposite equal	Perpendicular bisectors
Square	All equal	All 90°	Equal, perpendicular bisectors
Trapezium	One pair parallel	—	—
Kite	Two pairs of adjacent equal	One pair equal	Perpendicular

Parallelogram theorems (each with its converse)

• A diagonal divides a parallelogram into two congruent triangles (ASA/SSS).
• Opposite sides are equal; opposite angles are equal; diagonals bisect each other.
• Converse test: if one pair of opposite sides is equal and parallel, it is a parallelogram.

Mid-point theorem

The line joining the mid-points of two sides of a triangle is parallel to the third side and half of it. Converse: a line through the mid-point of one side parallel to another bisects the third side.

Example: In ΔABC, D and E are mid-points of AB and AC; BC = 10 cm → DE = 5 cm, DE ∥ BC. Joining mid-points of all sides of a quadrilateral gives a parallelogram (rhombus for a rectangle, rectangle for a rhombus).

Solved

ABCD is a parallelogram, ∠A = 70° → ∠B = 110°, ∠C = 70°, ∠D = 110°. Bisectors of adjacent angles meet at 90°.

Common mistakes

• Calling every quadrilateral with equal diagonals a rectangle (needs bisecting too)
• Using the mid-point theorem without both points being mid-points
• Forgetting the converse when asked to prove a parallelogram

Related: Lines and Angles.

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Frequently asked questions

Are these Quadrilaterals Class 9 Notes notes enough for the exam?

They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.

How should I revise Quadrilaterals Class 9 Notes?

Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.

What if I get stuck on a quadrilaterals class 9 question?

Type or photograph the exact question on DoubtPay AI, choose your class and language, and get a step-by-step answer with a diagram. You can also ask for a hint or have your own attempt checked. Packs start at ₹9 for 15 answers.