Posted on - 09-02-2017

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] .

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). .

**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.