PROPERITES OF QUADRILATERAL

quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

Sum of interior angles of a quadrilateral is 360.

There are six types of quadrilaterals. They are

Parallelogram

Definition of parallelogram :

A parallelogram is a quadrilateral which has opposite sides parallel.

Properties of parallelogram :

  • Opposite sides are equal in length
  • Opposite angles are equal in size.
  • Diagonals bisect each other.

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Rectangle

Definition of rectangle :

A rectangle is a parallelogram with four equal angles of 90 degree.

Properties of rectangle :

  • Opposite sides are equal and parallel.
  • Diagonals bisect each other.
  • Diagonals are equal in length.

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Rhombus

What is rhombus ?

A rhombus is a quadrilateral in which all sides are equal is length.

Properties :

  • Opposite sides are parallel.
  • Opposite angles are equal in size.
  • Diagonals bisect each other at right angles.
  • Diagonals bisect the angles at the vertex.

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Square

What is square ?

A square is a rhombus with four equal angles of 90.

Properties :

  • Opposite sides are parallel.
  • All sides are equal in length.
  • Diagonals bisect each other at right angles.
  • Diagonals bisect the angles at each vertex.
  • Diagonals are equal in length.

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Trapezium

What is trapezium ?

A trapezium is a quadrilateral which has a pair of parallel opposite sides.

Properties :

  • A trapezium has two parallel sides and two non parallel sides.
  • The diagonal of regular trapezium bisect each other.
  • The length of the midsegment is equal to half the sum of parallel bases.
  • Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non parallel side, add up to 180 degrees.

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Kite

Definition of kite :

A kite is a quadrilateral which has two pairs of adjacent sides equal in length.

Properties :

  • One diagonal is an axis of symmetry.
  • One pair of opposite angles are equal.
  • Diagonals cut each other at right angles.
  • One diagonal bisect one pair of angles at vertices.

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Properties of Quadrilaterals Quiz

Which of the following are true? Give reason for your answers.

Problem 1 :

A rectangle is a quadrilateral.

Solution :

True, since it has four sides, we can say rectangle is a quadrilateral.

Problem 2 :

A rectangle is a square.

Solution :

A rectangle may be a square sometimes, if all sides are equal. So, it is true.

Problem 3 :

A square is a rhombus.

Solution :

True, since all sides are equal in square and in rhombus.

Problem 4 :

A rhombus is a parallelogram.

Solution :

True, since opposite sides are parallel, we say rhombus is a parallelogram.

Quiz on properties of quadrilaterals

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