Theorem 8.6 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 8.6 class 9 Maths which is related to Chapter 8 Quadrilaterals Class 9 Mathematics. After understanding theorem 8.6, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 

 Theorem 8.6 Class 9

The diagonals of a parallelogram bisect each other.

Given 

 A parallelogram ABCD in which diagonal AC and BD intersect at O.

To Prove

OA=OC and OB=OD

Proof

In ∆OAB and ∆OCD,

We have AB∥DC and BD is transverse.

Hence ∠1= ∠4 (alternate angles)

AB=CD(opposite sides of ∥gm)

∠2= ∠3 (alternate angels AB∥DC and AC is the transversal)

So ,  ∆OAB and ∆OCD, (ASA congruence rule)

∴OA=OC and OB=OD (CPCT)

Hence proved

Related Topics

1. Theorem 8.5

2. Theorem 8.7