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Introduction

Quadrilateral of Class 9

NECESSARY CONDITIONS OF A PARALLELOGRAM

  • In a parallelogram, opposite sides are equal.
  • In a parallelogram, opposite angles are equal.
  • The diagonals of a parallelogram bisect each other.
  • A closed figure having four sides, four angles and four vertices is called a quadrilateral.
  • The sum of the four angles of a quadrilateral is 360°.

TYPES OF QUADRILATERALS

Trapezium: If one pair of opposite sides of a quadrilateral are parallel, then the quadrilateral is called a trapezium.

Parallelogram: If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.

Rectangle: In a parallelogram, if one angle is right angle, then the quadrilateral is called a rectangle.

Rhombus: In a parallelogram if all the four sides be equal, then the quadrilateral is a rhombus.

Square: In a quadrilateral if all the four sides are equal and one angle is right angle, then all the other three angles are also right angles. Such a quadrilateral is called a square.

SUFFICIENT CONDITIONS FOR A QUADRILATERAL TO BE PARALLELOGRAM

  • &If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
  • If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.
  • If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
  • A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.
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