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 split 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 degrees and vice-versa.
- In a square, diagonals are equal and bisect each other at 90 degrees 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.
Types of Quadrilaterals
A parallelogram is formed by joining the mid-points of the sides of a quadrilateral. Similarly, there are six basic types of quadrilateral including parallelogram. They are;
- Trapezium: one pair of opposite sides are parallel.
- Parallelogram: Both the opposite sides are parallel.
- Rectangle: All the angles are at 90 degrees and the opposite sides are parallel.
- Rhombus: All the sides are of equal length and opposite sides are parallel.
- Square: All the sides are equal and all angles are at 90 degrees.
- Kite: It has 2 pairs of equal-length sides and these sides are adjacent to each other.
Properties of Parallelogram
- Opposite sides of a parallelogram are equal
- Opposite angles of a parallelogram are equal
- The diagonals of a parallelogram bisect each other
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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