 # Quadrilaterals Class 9 Notes - Chapter 8

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.

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;

1. Trapezium: one pair of opposite sides are parallel.
2. Parallelogram: Both the opposite sides are parallel.
3. Rectangle: All the angles are at 90 degrees and the opposite sides are parallel.
4. Rhombus: All the sides are of equal length and opposite sides are parallel.
5. Square: All the sides are equal and all angles are at 90 degrees.
6. 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

### Important Questions

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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