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Summary

  • Sum of the angles of a quadrilateral is 360°.
  • A diagonal of a parallelogram divides it into two congruent triangles.
  • In a parallelogram,
    (i) opposite sides are equal
    (ii) opposite angles are equal
    (iii) diagonals bisect each other
  • A quadrilateral is a parallelogram, if
    (i) opposite sides are equal
    (ii) opposite angles are equal
    (iii) diagonals bisect each other
    (iv) a pair of opposite sides is equal and parallel
  • Diagonals of a rectangle bisect each other and are equal and vice-versa.
  • Diagonals of a rhombus bisect each other at right angles and vice-versa.
  • Diagonals of a square bisect each other at right angles and are equal, and vice-versa.
  • The line-segment joining the midpoints of any two sides of a triangle is parallel to the third side and is half of it.
  • A line through the mid-point of a side of a triangle parallel to another side bisects the third side.
  • The quadrilateral formed by joining the midpoints of the sides of a quadrilateral, is a parallelogram.
     
    Rectangle A quadrilateral with all angles 90 degrees
    Parallelogram A quadrilateral with both pairs of opposite sides parallel
    Rhombus A quadrilateral with all sides equal
    Square A rectangle with all sides equal
    Trapezium A quadrilateral with one pair of opposite sides parallel
    Kite A quadrilateral with two pairs of adjacent sides of equal length




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