Quadrilaterals

Quadrilateral

Quadrilateral

A quadrilateral is a closed figure bounded by four line segments.
    A quadrilateral ABCD has
  1. four vertices (A,B,C and D)
  2. four sides (AB, BC, CD and DA)
  3. four angles (∠A, ∠B, ∠C and ∠D)
  4. two diagonals (AC and BD)

Adjacent sides

Two sides of a quadrilateral having a common end-point are called adjacent or consecutive sides. There are four pairs of it.
In the quadrilateral (AB,BC), (BC,CD), (CD,DA) and (DA,AB) are such sides.

Opposite sides

Two sides of a quadrilateral having no common end-point are called opposite sides. There are two pairs of it.
In the quadrilateral (AB,CD) and (BC,DA) are such sides.

Adjacent angles

Two angles of a quadrilateral having a common side are called adjacent or consecutive angles. There are four pairs of it.
In the quadrilateral (∠A,∠B), (∠B,∠C), (∠C,∠D) and (∠D,∠A) are such angles.

Opposite angles

Two angles of a quadrilateral having no common side are called opposite sides. There are two pairs of it.
In the quadrilateral (∠A,∠C) and (∠B,∠D) are such sides.

Various types of quadrilaterals

Parallelogram

Parallelogram

A quadrilateral in which opposite sides are parallel is called a parallelogram.
ABCD is a parallelogram. AB||CD and BC||DA.

Properties of a parallelogram

  • opposite sides are equal
  • opposite angles are equal
  • diagonals bisect the parallelogram
Rectangle

Rectangle

A parallelogram in which all the angles are 90° is called a rectangle.
ABCD is a rectangle.

Properties of a rectangle

  • opposite sides are equal
  • each angle measures 90°
  • diagonals are equal
Square

Square

A rectangle in which all sides are equal is called a square.
ABCD is a square.

Properties of a square

  • all sides are equal
  • each angle measures 90°
  • diagonals are equal
  • diagonals intersect at 90°
Rhombus

Rhombus

A parallelogram in which all sides are equal is called a rhombus.
Ab=CD=DA=AB
ABCD is a rhombus.

Properties of a rhombus

  • opposite sides are parallel
  • all sides are equal
  • diagonals bisect each other at right angles
Trapezium

Trapezium

A quadrilateral in which two opposite sides are parallel is called a trapezium.
ABCD is a Trapezium.
AB||DC.
If the non parallel sides are equal then the trapezium is called isosceles trapezium.




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