Question

There is a theorem in parallelogram where opposite angles are equal, prove it.

Answer 1

According to the question,

In a parallelogram, opposite angles are equal.

Given: Parallelogram $ABCD$

To prove: $\angle A=\angle C$ and $\angle B=\angle D$

Proof :

In parallelogram $ABCD$
Consider,

$AD\left|\right|BC$ and$AB$ is transversal

$\angle A+\angle B=180°$[interior Angles on the same side of transversal]… (i)

Now, consider $AB\left|\right|DC$ and $BC$transversal

$\angle B+\angle C=180°$[interior Angles on the same side of transversal]… (ii)

From (i) and (ii) we get ;

$\angle A+\angle B=\angle B+\angle C$

$\angle A+\angle B-\angle B=\angle C$

$\angle A=\angle C$

Similarly, $\angle B=\angle D$

Hence, it is proved that opposite angles of a parallelogram are equal