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Subject  >  Math  >  Geometry  >  Parallelograms

Parallelograms

Introduction
       We are familiar with plane figures bounded by straight line segments as sides. They are known as Polygons. Polygon is a word of Greek origin. It means figure with many angles implying many sides.
Parallelograms
       Parallelogram is a quadrilateral whose opposite sides are parallel and equal. A rectangle, a rhombus and a square are considered as parallelograms.
Theorem1
      The diagonals of a parallelogram bisect each other.
Sufficient Conditions for a Quadrilateral to be a Parallelogram
      If both pairs of opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram.
Theorem2
      If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.
Theorem3
      A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel.
Special Parallelograms
      Rectangles, rhombuses and squares belong to the set of parallelograms.
Theorem4
      Recall that the diagonals of a parallelogram bisect each other. Since a rectangle is also a parallelogram, the diagonals of a rectangle also bisect each other.
Converse of Theorem4
      If two diagonals of a parallelogram are equal, it is a rectangle.
Theorem5
      The diagonals of a rhombus are perpendicular to each other.
Converse of Theorem5
      If the diagonals of a parallelogram are perpendicular then it is a rhombus.
Theorem6
      The diagonals of a square are equal and perpendicular to each other.
Converse of Theorem6
      If in a parallelogram, the diagonals are equal and perpendicular, then it is a square.
Theorem7
      The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
Converse of Theorem7
      A straight line drawn through the mid-point of one side and parallel to another side of a triangle bisects the third side.
Theorem8
      If there are three or more parallel lines and the intercepts made by them on one transversal are equal, the corresponding intercepts of any transversal are also equal.
Summary
       Quadrilateral : A plane closed figure formed by four line segments is called a quadrilateral.
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