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Monday, February 17, 2014

10 IMPORTANT THEOREMS FOR QUADRILATERALS

Since we have been studying about quadrilaterals in Class 9,I thought to compile the theorems related to quadrilaterals. This might just help other students to get them done at a glance!

What is a quadrilateral?

 As Euclidean geometry is the best accepted form of Geometry in today's world,we will go with the          definition from Euclidean geometry itself.According to Euclidean Plane Geometry,a quadrilateral is a polygon with four edges and four vertices.


Origin of the Word

The origin of the word "quadrilateral" is the two Latin words quadri, a variant of four, and latus,     meaning "side."

Important note : The sum of all the angles of a quadrilateral always give 360° when added together.

Different types of Quadrilaterals


The Theorems


  • If the quadrilateral is a parallelogram,the two pairs of opposite sides are equal.
  • Converse : If the two pairs of opposite sides of a quadrilateral are equal,it is a parallelogram.
  • Opposite angles of a parallelogram are equal.
  • If in a quadrilateral,each pair of opposite angles are equal,it is a parallelogram.
  • If one pair of sides of a quadrilateral are equal and parallel to each other,it is a parallelogram.
  • If the diagonals of a quadrilateral bisect each other,it is a parallelogram.
  • The diagonals of a parallelogram bisect each other.
  • Converse : The diagonals of a parallelogram divides in into congruent triangles. (Each diagonal divides the parallelogram into two congruent triangles)
Mid - Point Theorem
  • The line segment that joins the mid-points of two sides of a triangle is parallel to the third side and half of the third side in measure.
  • Converse : The line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.






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