- 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
- Opposite angles
- 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). .
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.