## Monday, 4 July 2011

### NCERT CBSE Class 9th Maths : Properties of Parallelogram

Properties of parallelogram :

A quadrilateral is a closed figure formed by four line segments and

A parallelogram is a quadrilateral in which the opposite sides are parallel to each other.

Property 1: In a parallelogram, the opposite sides are of equal length

Property 2: In a parallelogram, the opposite angles are of equal measure

Property 3: The diagonals of a parallelogram bisect each other.

Property 4: If the opposite sides of a quadrilateral are of equal length, then the quadrilateral is a parallelogram.

Property 5: If the opposite angles in a quadrilateral are of equal measure, then the quadrilateral is a

parallelogram.

Property 6: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Theorem 12: A quadrilateral is a parallelogram if one pair of opposite sides are parallel and equal.

Property 7: If there are three or more parallel lines and the intercepts made by them on a transversal are
equal, then the corresponding intercepts on any other transversal are also equal

Property 8: In a triangle, the line joining the mid points of two sides is parallel to the third side and is equal
to one half of it.

Property 9: In a triangle, the line drawn through the mid-point of one side, parallel to another side, bisects the
third side.

Theorem 13: The medians of a triangle are concurrent and the point of concurrency divides each median in

Theorem 14: Parallelograms on the same base and between the same parallels are equal in area.

Theorem 15: Triangles on the same base and between the same parallels are equal in area. Theorem 16: If
a ray stands on a line, then the sum of the adjacent angles so formed is 180°.

Theorem 17: If two lines intersect, then the vertically opposite angles are of equal measure.

Theorem 18: The sum of the three angles of a triangle is 180°.

Theorem 19: The angles opposite to equal sides of a triangle are equal.

Theorem 20: The side opposite to the larger of two angles in a triangle is longer than the side opposite to the
smaller angle.

Theorem 21: A parallelogram is a rhombus if its diagonals are perpendicular.