Theorem 8.1 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 8.1 class 9 Maths which is related to Chapter 8 Quadrilaterals Class 9 Mathematics. After understanding theorem 8.1, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 

 Theorem 8.1 Class 9

A diagonal of a parallelogram divides it into two congruent triangles.

Given 

A parallelogram ABCD with diagonal AC

To Prove

∆ABC≅∆ADC 

Proof 

Let ABCD be a parallelogram and AC be diagonal. Diagonal AC divides parallelogram ABCD into two triangles namely ∆ABC and ∆ADC.

In  ∆ABC and ∆ADC, BC∥AD and AC is a transversal.

so,  ∠BCA= ∠DAC (pair of alternate angles)

also,  AB∥DC and AC is a transversal.

So, ∠BAC= ∠DCA (pair of alternate angles)

And, AC=CA (common)

So, ∆ ABC ≅ ∆ CDA (ASA rule)

Diagonal AC divides parallelograms ABCD into two congruent triangles ABC and CDA. 

∆ ABC ≅ ∆ CDA Hence proved.

Related Topics

1. Theorem 8.2