Quadrilaterals

Board: GSEB Class: 9

Chapter Overview

A quadrilateral has four sides, four angles, and two diagonals. Sum of interior angles = 360°. Types: parallelogram (opposite sides parallel and equal), rectangle (parallelogram with right angles), rhombus (all sides equal, diagonals perpendicular), square (all sides equal, all angles 90°), trapezium (one pair of parallel sides). Properties: in a parallelogram, opposite sides are equal, opposite angles are equal, diagonals bisect each other. The Midpoint Theorem: the segment joining midpoints of two sides of a triangle is parallel to the third side and half its length.

Topics Covered

Quadrilateral Types
Parallelogram Properties
Rectangle Properties
Rhombus Properties
Square Properties
Trapezium
Midpoint Theorem
Diagonals Properties

Key Formulas

Sum of angles = 360°

Parallelogram: AB = CD, AD = BC

Parallelogram: diagonals bisect each other

Midpoint theorem: PQ || BC, PQ = BC/2

Real-World Applications

Applications: Architecture, floor tile design, structural engineering, computer graphics, construction.

Study Tips

Tip: Learn all parallelogram properties systematically

Tip: Practice the midpoint theorem

Tip: Draw labeled diagrams for problems