Understanding Quadrilaterals

Quadrilaterals are fundamental shapes in geometry, consisting of four-sided polygons. They play a crucial role in both theoretical mathematics and practical applications. Understanding quadrilaterals and their properties is essential for solving various geometry problems and real-world scenarios.

Polygon

A polygon is a closed shape made by connecting three or more straight lines.

Examples of polygons are shown below:

Types of Polygons: Convex and Concave Polygons

Types of Polygons: Regular and Irregular Polygons

Properties of Polygons

Here is the properties of polygons with 'n' sides:

1. Sum of interior angles = (n − 2) × 180°
2. Sum of exterior angle = 360°
3. Each interior angle of a regular polygon = (n − 2) × 180°/n
4. Each exterior angle of a regular polygon = 360°/n
5. Interior angle + exterior angle = 180°

Quadrilateral

A quadrilateral is a four-sided flat polygon whose sum of interior angles is 360°.

Types of Quadrilaterals

Parallelogram

A parallelogram is a four-sided quadrilateral where opposite sides are parallel.

Important properties:

i. Opposite sides are of the same length.
ii. Opposite angles are equal.
iii. The diagonals (lines connecting opposite corners) bisect each other.

Square

A square is a special kind of parallelogram whose all sides are equal.

Important properties:

i. All sides are the same length.
ii. All angles are 90° (like a perfect "L" shape).
iii. The diagonals are of the same length and bisect each other at a right angle.

Rectangle

A rectangle is another special kind of parallelogram in which opposite sides are equal and all angles are equal to a right angle.

Important properties:

i. Opposite sides are equal and parallel.
ii. All angles are 90°.
iii. The diagonals are of the same length and bisect each other.

Rhombus

A rhombus is a parallelogram with all sides equal.

Important properties:

i. All sides are equal.
ii. Opposite angles are equal.
iii. The diagonals bisect each other at right angles but they are not necessarily of the same length.

Trapezium

A trapezium is a quadrilateral with only one pair of opposite sides that are parallel and another pair is non-parallel.

In a trapezium, the sum of each pair of co-interior angles is 180°.

∠A + ∠D = 180°and ∠B + ∠C = 180°

Isosceles Trapezium

This is a special trapezium where the non-parallel sides are equal in length.

Important properties:

i. The angles where the base of the trapezium meets are equal.
ii. The diagonals are equal.

Kite

A kite is a quadrilateral where two pairs of adjacent sides are equal in length.

Important properties:

i. Opposite sides are not equal.
ii. The diagonals intersect each other at right angles.
iii. One pair of opposite angles is equal.
iv. One diagonal bisects the other.