# NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## 8. 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 QuadrilateralA quadrilateral is a four-sided polygon with four angles. There are many kinds of quadrilaterals.The five most common types are the parallelogram, 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 divides into two congruent triangles Called a ParallelogramA 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 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 equalThe opposite angles of a rhombus are equalThe diagonals of a rhombus bisect each other at right angles. Rhombus is a Parallelogram 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 equalEach 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 7 Square A quadrilateral, all whose sides are equal and all whose angles are right angles.Properties of square are:All the sides of a square are equal.Each of the angle՚s measures 90.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 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 thetwo sides of the triangle are parallel to the thirdside(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