Quadrilaterals Types and Properties

Quadrilaterals

Definition

• A quadrilateral is a polygon with four sides and four vertices.

Types of Quadrilaterals

• A rectangle is a quadrilateral with all angles being right angles (90 degrees) and opposite sides of equal length.
• A square is a quadrilateral with all angles being right angles (90 degrees) and all sides of equal length.
• A rhombus is a quadrilateral with all sides of equal length, but not necessarily right angles.
• A trapezoid (or trapezium) is a quadrilateral with at least two pairs of opposite sides that are not equal in length.
• A kite is a quadrilateral with two pairs of adjacent sides of equal length, and one pair of opposite angles that are equal.
• An irregular quadrilateral is a quadrilateral that does not fit into any of the above categories.

Properties of Quadrilaterals

• The sum of the interior angles of a quadrilateral is always 360 degrees.
• The diagonals of a quadrilateral intersect each other, and the sum of the lengths of the diagonals is greater than the sum of the lengths of any two opposite sides.

Theorems and Formulae

• The midpoint theorem states that the line segment joining the midpoints of two sides of a quadrilateral is parallel to the third side and half its length.
• The area of a quadrilateral can be calculated using the formula: Area = (b × h) / 2, where b is the base and h is the height.

Learn about the definition and types of quadrilaterals, including rectangles, squares, rhombi, and trapezoids.