Mathematics · Class 9
Quadrilaterals
Parallelogram theorems, mid-point theorem, and quadrilateral proofs.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Quadrilaterals are four-sided polygons. Class 9 covers types (parallelogram, rectangle, rhombus, square, trapezium, kite), their properties, and the mid-point theorem.
Parallelogram Properties
- Opposite sides parallel and equal
- Opposite angles equal
- Diagonals bisect each other
- Adjacent angles supplementary
Special Quadrilaterals
- Rectangle: parallelogram with each angle 90°
- Rhombus: parallelogram with all sides equal; diagonals perpendicular
- Square: both rectangle and rhombus
- Mid-point theorem: join of mid-points of two sides is parallel to third side and half its length
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Parallelogram angles
In parallelogram ABCD, ∠A = 70°. Find ∠B and ∠C.
- 1Adjacent angles supplementary: ∠B = 180° − 70° = 110°
- 2Opposite angles equal: ∠C = ∠A = 70°
Answer
∠B = 110°, ∠C = 70°
Example 2: Mid-point theorem
In ΔABC, D and E are mid-points of AB and AC. If BC = 10 cm, find DE.
- 1By mid-point theorem, DE ∥ BC
- 2DE = ½ BC = 5 cm
Answer
DE = 5 cm
Key Points to Remember
- ✓ Sum of angles of quadrilateral = 360°
- ✓ Diagonals of rhombus bisect at 90°
- ✓ Square has all properties of rectangle and rhombus
Exam Tips
- • State which property you use in proofs
- • Mark parallel sides and equal angles in parallelograms
- • Mid-point theorem often appears in proofs
Practice MCQs — Quadrilaterals
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Diagonals of a parallelogram: