What is a quadrilateral?
A quadrilateral is a closed figure with four straight sides. The sum of all the interior angles of a quadrilateral is 360 degree. Quadrilaterals class 9 notes are provided here to help learners prepare for their examination in an easy and effective manner.
The diagonal splits a parallelogram into 2 triangles which are congruent. Opposite sides and angles of a parallelogram are equal. Also, diagonals of a parallelogram always bisecting each other.
- A quadrilateral is a parallelogram, if either opposite sides or opposite angles are equal or diagonals are bisecting each other or pair of opposite sides are parallel and equal.
- In a rectangle, diagonals are equal and bisect each other and vice-versa.
- In a rhombus, diagonals bisect each other at 90 degree and vice-versa.
- In a square, diagonals are equal and bisect each other at 90 degree and vice-versa.
- In a triangle, the line joining midpoints of any two sides is parallel to the 3rd side and is half of it.
A parallelogram is formed by joining the mid-points of the sides of a quadrilateral. Some examples of parallelogram are:
In a trapezium, one pair of opposite sides of quadrilateral is parallel. If both pairs of opposite sides of quadrilaterals are parallel then it is called parallelogram. If one angle of a parallelogram is a right angle then it is called a rectangle. If all the sides of a parallelogram are equal then it is called a rhombus. If all the sides of a parallelogram are equal and angle is 90 degree then it is called a square. A square is both rhombus and rectangle. A trapezium is not a parallelogram but a parallelogram is a trapezium. Also, a rhombus or rectangle is not a square.
Q.1) Prove that the diagonals of a rhombus are perpendicular to each other.
Q.2) In the figure below, 2 parallel lines l and m are intersected by a transversal p. Prove that the quadrilateral formed by the bisectors of interior angles is a rectangle.
Q.3) Prove that the bisectors of the angles of a parallelogram form a rectangle.
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