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Basic Theory - 4 on Plane Geometry for Upcoming Bank and SSC Exams

Posted on - 09-02-2017

QA Math Plane Geometry

Bank PO

Fig.12.

  • If one pair of opposite sides of a quadrilateral are parallel, then it is called a trapezium. In the figure alongside, AD is parallel to BC. .
  • Area of a trapezium = 1/2 x Sum of parallel sides x distance between them = 1/2 x (AD + BC) x AF
  • If the midpoints of the two non-parallel sides are joined, it is equal in length to the average of the two parallel sides i.e., PQ = 1/2 [AD + BC] .

    Parallelogram

    A quadrilateral in which opposite sides are parallel is called a parallelogram. In a parallelogram .

    • Opposite sides are equal
    • Opposite angles are equal
    • Each diagonal divides the parallelogram into two congruent triangles. .
    • Sum of any two adjacent angles is 180°
    • The diagonals bisect each other

      Conversely, if in a quadrilateral

      (a) the opposite sides are equal or

      (b) the opposite angles are equal or

      (c) the diagonals bisect each other or

      (d) a pair of opposite sides are parallel and equal such a quadrilateral is a parallelogram. .

      • The area of a parallelogram = base x height = CD x AE
      • If any one angle of a parallelogram is a right angle, then it becomes a rectangle (i.e., all four angles are 90° in measurement). .

        Rhombus

        Fig.14.

        A rhombus is a parallelogram in which a pair of adjacent sides are equal (all four sides of a rhombus are equal). Since a rhombus is a parallelogram, all the properties of a parallelogram apply to a rhombus. Further, in a rhombus, the diagonals bisect each other perpendicularly. Area of a rhombus = Half the product of the two diagonals. .

        Side of a rhombus = x Sum of squares of the diagonals.

         
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