CBSE Class 8 Mathematics Quadrilaterals Notes Set 01

Polygons and Their Angles

A polygon is a closed figure made of line segments. A quadrilateral has four sides, four vertices and two diagonals. A polygon is convex if all its angles are less than 180 degrees and concave if at least one angle is a reflex angle.
Sum of the interior angles of an n-sided polygon = (n - 2) x 180 degrees; for a quadrilateral this is 360 degrees. The exterior angles (one at each vertex) of any convex polygon add up to 360 degrees. In a regular polygon every exterior angle = 360/n.

Kinds of Quadrilaterals

Trapezium: exactly one pair of parallel sides. In an isosceles trapezium the non-parallel sides are equal.
Kite: two pairs of equal adjacent sides; the diagonals meet at right angles and one diagonal bisects the other.
Parallelogram: both pairs of opposite sides parallel. Opposite sides and opposite angles are equal, adjacent angles add to 180 degrees and the diagonals bisect each other.
Rhombus: a parallelogram with all sides equal; diagonals bisect each other at right angles.
Rectangle: a parallelogram with all angles 90 degrees; diagonals are equal.
Square: a rectangle with all sides equal; diagonals are equal and cross at right angles.

How the Shapes Are Related

Every square is a rectangle and a rhombus, every rectangle and rhombus is a parallelogram, and every parallelogram is a quadrilateral. To identify a shape, list its properties and match the strongest definition.

Worked example: the diagonals of a rhombus are 12 cm and 16 cm. Half-diagonals 6 and 8 meet at 90 degrees, so a side is 10 cm and the perimeter is 40 cm.