Quadrilaterals: Definition and Meaning, Properties of Quadrilaterals (For CBSE, ICSE, IAS, NET, NRA 2022)

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Quadrilaterals

  • Quadrilateral in geometry can be defined as a closed, two-dimensional shape with four straight sides.
  • According to Euclidean plane geometry, a quadrilateral can be defined as a polygon with four edges (sides) and four vertices (corners) .
  • Other names for quadrilateral include:
    • Quadrangle (in analogy to triangle)
    • Tetragon (in analogy to pentagon)
    • 5-sided polygon
    • Hexagon
    • (6-sided polygon)
    • 4-gon (in analogy to k-gons for arbitrary values of k)
  • In our day today life there exist several numbers of things with shape of quadrilaterals.
    • Chess board
    • A deck of cards
    • A kite
    • A tub of popcorn

Properties of a Quadrilateral

  • A quadrilateral contains 4 sides, 4 angles and 4 vertices.
  • A quadrilateral can be regular or irregular.
  • The sum of all the interior angles of a quadrilateral is 360°.

Types of Quadrilateral

Types of Quadrilateral
Name of the QuadrilateralPictureProperties
Square Shape
Illustration 2 for Types_of_Quadrilateral
Illustration 3 for Types_of_Quadrilateral
RectangleOpposite sides are parallel and equal.

All angles are equal measuring 90°.

Rhombus
Rhombus Shape
All sides are equal.

Opposite angles are equal.

Trapezoid
Trapezoid Shape
Opposite sides are parallel.

Adjacent angles add up to 180°.

Parallelogram
Parallelogram Quadrilateral
Opposite sides are parallel and equal.

Opposite angles are equal.

Quadrilateral Polygon

It has four vertices or corners.

Different types are Parallelogram, Square, Rectangle, etc.

Polygon with Four Corners
Polygon with Four Vertices or Corners

Kite

Properties of Kite

  • Diagonals of a kite intersect each other at right angles.
  • Two pairs of adjacent sides are of equal length.
  • One of the diagonals is the perpendicular bisector of another.
  • Angles between unequal sides are equal.
Kite-A Quadrilateral

(i) In quadrilateral PQRS, the sides PQ = QR and PS = ₹ . Here the adjacent pair of sides are equal in length and hence PQRS is a special type of quadrilateral known as a kite.

In

QS are common

Hence by SSS rule of congruency

Also, we have in

Therefore

Thus, by ASA rule of congruency

Also, we have by Linear Pair

(ii) Since

using CPCT

Thus, QS bisects PR at O.

Hence one of the diagonals is the perpendicular bisector of another.

(iii) Since

using CPCT

Hence the angles between unequal sides are equal.

(iv) Area of a kite

Area of a Kite

If the length of both the diagonals are given as A and B, then area can be given as:

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