Understanding Quadrilaterals

Understanding Quadrilaterals

Definition

• A quadrilateral is a polygon with four sides
• It can be convex or concave
• A quadrilateral can be regular or irregular

Properties

• Sum of interior angles: 360°
• Number of diagonals: 2 (AC and BD in a quadrilateral ABCD)
• Types of quadrilaterals:
  • Rectangle: all angles are right angles (90°)
  • Square: all sides are equal and all angles are right angles
  • Rhombus: all sides are equal, but not all angles are right angles
  • Trapezium: at least two sides are not equal
  • Kite: two pairs of adjacent sides are equal

Types of Quadrilaterals

Rectangle

• Opposite sides are equal and parallel
• All angles are right angles (90°)
• Diagonals are equal and bisect each other

Square

• All sides are equal
• All angles are right angles (90°)
• Diagonals are equal and bisect each other at 90°

Rhombus

• All sides are equal
• Opposite angles are equal
• Diagonals are perpendicular and bisect each other

Trapezium

• At least two sides are not equal
• Opposite sides are not parallel
• Diagonals are not equal

Kite

• Two pairs of adjacent sides are equal
• One pair of opposite angles are equal
• Diagonals are perpendicular

Understanding Quadrilaterals

Definition

• A quadrilateral consists of four sides and can be classified as convex (bulging outward) or concave (caving inward).
• Quadrilaterals can be categorized as regular (sides and angles are equal) or irregular (sides and angles are not equal).

Properties

• The total sum of the interior angles in any quadrilateral is 360°.
• Every quadrilateral contains 2 diagonals.
• Various types of quadrilaterals include:
  • Rectangle: Features four right angles (90°).
  • Square: All sides are equal, and all angles are right angles.
  • Rhombus: All sides are equal while angles are not necessarily right.
  • Trapezium: Characterized by at least two sides that are not equal.
  • Kite: Presents two pairs of adjacent sides that are equal.

Types of Quadrilaterals

Rectangle

• Opposite sides are both equal in length and parallel to each other.
• Contains four right angles (90°).
• The diagonals are equal in length and bisect one another.

Square

• All sides have the same length.
• Features four right angles (90°).
• Diagonals are equal in length and intersect at right angles (90°).

Rhombus

• All sides are of equal length.
• Opposite angles are equal in measurement.
• Diagonals intersect at right angles and bisect each other.

Trapezium

• Contains at least two sides that differ in length.
• Opposite sides are not parallel to each other.
• Diagonal lengths are unequal.

Kite

• Contains two pairs of adjacent sides that are equal in length.
• One pair of opposite angles are equal.
• The diagonals intersect perpendicularly.

Quadrilaterals Overview

• A quadrilateral is a polygon characterized by four sides and four vertices.
• The total measure of the interior angles in any quadrilateral is 360°.

Properties of Quadrilaterals

• Quadrilaterals can be classified as either convex or concave.
• In convex quadrilaterals, all internal angles are less than 180°.
• Concave quadrilaterals have one or more angles that exceed 180°.

Types of Quadrilaterals

• Rectangle: All sides are equal in length, with right angles (90°) at each corner.
• Square: A specific type of rectangle where all sides are equal.
• Rhombus: All sides are of equal length, but angles are not necessarily right angles.
• Trapezoid (or Trapezium): Defined by having one pair of opposite sides that are parallel.
• Kite: Features two pairs of adjacent sides of equal length, and one pair of equal opposite angles.

Diagonals of Quadrilaterals

• A diagonal connects two non-adjacent vertices of a quadrilateral.
• In most quadrilaterals, the diagonals bisect each other; however, this does not apply to kites.
• For rectangles, diagonals are equal in length and intersect at right angles.

Angles in Quadrilaterals

• The interior angles of a quadrilateral total 360°, which can be represented as: 360° = a + b + c + d.
• Each angle in a quadrilateral contributes to the overall total of 360°.