Theorem 8.7 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 8.7 class 9 Maths which is related to Chapter 8 Quadrilaterals Class 9 Mathematics. After understanding theorem 8.7, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 Theorem 8.7 Class 9

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Given 

ABCD is a quadrilateral whose diagonals AC and BD bisect each other.

OA=OC and OB=OD

To Prove

ABCD is a parallelogram.

Proof 

In ∆AOB and ∆COD

OA=OC                     (Given)

OB=OD                     (Given)

∠AOB=∠COD        (Vertically opposite angles)

∴ ∆AOB≅∆COD    (By SAS congruence rule)

Then ∠ODC= ∠OBA (By CPCT)

But these are alternate angles that are formed when transversal BD intersects lines AB and DC.

∴AB∥DC 

Similarly, we can prove that BC∥AD

  Hence, ABCD is a parallelogram. 

Hence proved. 

Related Topics

1. Theorem 8.6

2. Theorem 8.8