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NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 8
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 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:
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. |
5 | Rhombus | Rhombus is a parallelogram in which any pair of adjacent sides is equal. Properties of a rhombus:
|
6 | Rectangles | A parallelogram which has one of its angles a right angle is called a rectangle. Properties of a rectangle are:
|
7 | Square | A quadrilateral, all whose sides are equal and all whose angles are right angles. Properties of square are:
The diagonals of a square are equal. |
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 are 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 |