Question

Prove that in a parallelogram the opposite angles are equal .

Answer 1

In this given figure,

$ABCD$ is parallelogram.

Proof;

In parallelogram $ABCD$,

Cosider,

$AD||BC$ and $AB$ is traversal

$\angle A+\angle B={180}^0$ [Co-int Angles].......(1)

Now, Consider $AB||DC$ are $BC$ transversal

$\angle B+\angle C={180}^0$ [Co- int, Angles].............(2)

From $\left(1\right)$ and $\left(2\right)$ we get,

$\begin{array}{c}\angle A+\angle B=\angle B+\angle C\\ \angle A=\angle C\\ \angle B=\angle D\end{array}$

Hence,proved