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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 
the radio 2:1.


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.

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