NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 8

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8. Quadrilaterals

Quadrilaterals
S.no	Terms	Descriptions
1	Quadrilateral	A quadrilateral is the union of four line-segments determined by four distinct coplanar points of which no three are collinear and the line-segments intersect only at end points. For ABCD to be quadrilateral, following condition are required a) The four points A, B, C and D must be distinct and co-planar. b) No three of points A, B, C and D are co-linear. c) Line segments i.e. AB, BC, CD, DA intersect at their end points only. A Quadrilateral Loading image••• A quadrilateral is a four-sided polygon with four angles. There are many kinds of quadrilaterals. The five most common types are the parallelo gram, the rectangle, the square, the trapezoid, and the rhombus
2	Angle Property of Quadrilateral	1) Sum of all the interior angles is 360° 2) Sum of all the exterior angles is 360°
3	Parallelogram	A quadrilateral which has both pairs of opposite sides parallel is called a parallelogram. its properties are: The opposite sides of a parallelogram are equal. The opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other. The diagonal of a parallelogram divide into two congruent triangles Called a Parallelogram Loading image••• A quadrilateral is said to a parallelogram if Opposite sides are equal OR Opposite angles are equal OR Diagonal bisects each other OR A pair of opposite are parallel and equal
4	Trapezium	A quadrilateral which has one pair of opposite sides parallel is called a trapezium. Called a Trapezium Loading image•••
5	Rhombus	Rhombus is a parallelogram in which any pair of adjacent sides is equal. Properties of a rhombus: All sides of a rhombus are equal The opposite angles of a rhombus are equal The diagonals of a rhombus bisect each other at right angles. Rhombus is a Parallelogram Loading image•••
6	Rectangles	A parallelogram which has one of its angles a right angle is called a rectangle. Properties of a rectangle are: The opposite sides of a rectangle are equal Each angle of a rectangle is a right-angle. The diagonals of a rectangle are equal. The diagonals of a rectangle bisect each other. Properties of a Rectangle Loading image•••
7	Square	A quadrilateral, all of whose sides are equal and all of whose angles are right angles. Properties of square are: All the sides of a square are equal. Each of the angles measures 9O. The diagonals of a square bisect each other at right angles. The diagonals of a square are equal. A Quadrilateral, All of Whose Sides Are Loading image•••
8	Important points about quadrilaterals	a) A square is always a parallelogram. b) A square is always a rectangle. c) A rhombus can be square. d) A rectangle has four right angles.
9	Mid-point Theorems for Triangles	1)The line segment joining the mid-points of the two sides of the triangle is parallel to the third side 2) A line drawn through mid-point of one side of a triangle and parallel to another side bisect the third side of the triangle