Classify quadrilaterals

key notes :

Definition of a Quadrilateral:

• A quadrilateral is a polygon with four sides and four angles.
• The sum of the interior angles of a quadrilateral is always 360°.

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Types of Quadrilaterals:

Quadrilaterals can be classified based on their sides and angles into different types. The main types include:

• Square:

• All four sides are equal.
• All angles are 90°.
• Diagonals are equal and bisect each other at right angles.
• Rectangle:

• Opposite sides are equal in length.
• All angles are 90°.
• Diagonals are equal in length.
• Rhombus:

• All four sides are equal.
• Opposite angles are equal.
• Diagonals bisect each other at right angles but are not necessarily equal in length.
• Parallelogram:

• Opposite sides are parallel and equal in length.
• Opposite angles are equal.
• Diagonals bisect each other but are not necessarily equal in length.
• Trapezoid (Trapezium in UK):

• Only one pair of opposite sides is parallel.
• The non-parallel sides are called the legs.
• Kite:

• Two pairs of adjacent sides are equal.
• One pair of opposite angles are equal.
• Diagonals intersect at right angles.

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Properties of Quadrilaterals:

• Angles:
  • The sum of the interior angles of any quadrilateral is always 360°.
  • The sum of the exterior angles of any quadrilateral is always 360°.
• Diagonals:
  • In general, diagonals do not necessarily bisect each other unless the quadrilateral is a special type (like a rectangle or rhombus).
  • Diagonals of specific quadrilaterals have different properties: they can bisect angles, intersect at right angles, or be equal in length.

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Classifying Quadrilaterals Based on Symmetry:

• Some quadrilaterals have lines of symmetry, while others do not.
• A square has 4 lines of symmetry, a rectangle has 2, and a rhombus has 2.

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Special Properties:

• Square and Rectangle: Both are types of parallelograms with specific properties (e.g., right angles in rectangles and equal sides in squares).
• Rhombus and Parallelogram: Both have opposite sides equal and parallel, but a rhombus has equal sides and a parallelogram may not.
• Kite: The diagonals of a kite intersect at right angles and one diagonal bisects the other.

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Classification Based on Angles:

• Quadrilaterals can also be classified based on their angles:
  • Right Angled Quadrilaterals (Square, Rectangle).
  • Oblique Quadrilaterals (Parallelogram, Rhombus).

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