Theorem 8.2 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 8.2 class 9 Maths which is related to Chapter 8 Quadrilaterals Class 9 Mathematics. After understanding theorem 8.2, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 

 Theorem 8.2 Class 9

In a parallelogram, opposite sides are equal.

Given 

A parallelogram ABCD

To Prove

AB=CD and DA=BC

Construction 

Join AC

Proof 

Since ABCD is a parallelogram. So AB∥DC and AD∥BC.

Now,  AD∥BC and transversal AC intersect them at A and C respectively.

∠DAC=∠BCA ………….(i) (Alternate interior angles)

Again AB∥DC and transversal AC intersects at A and C respectively.

∴ ∠BAC=∠DCA ………..(ii)(Alternate interior angles)

Now, in ∆ADc and ∆CBA, we have

∠DAC=∠BCA                      [from (i)]

AC=AC (common side)

And ∠DCA=∠BAC               [from (ii)]

So by ASA criterion of congruence

∆ADC≅∆CBA 

⟹  AD=CB and DC=BA (∵corresponding parts of congruence triangles are equal )

Hence proved

Related Topics

1. Theorem 8.1

2. Theorem 8.3