Question

Show that opposite angles of parallelogram are equal.

Answer 1

Here, $ABCD$ is a parallelogram with $AC$ as its diagonal.

We know, in parallelogram opposites sides are parallel.

So, $AB\parallel DC$ and $AD\parallel BC$

Since, $AB\parallel DC$ and $AC$ is the transversal

$\Rightarrow$ $\angle BAC=\angle DCA$ ---- ( 1 ) [ Alternate angles ]

Similarly, $AD\parallel BC$ and $AC$ is the transversal.

$\Rightarrow$ $\angle DAC=\angle BCA$ ---- ( 2 ) [ Alternate angles ]

Adding ( 1 ) and ( 2 ),

$\Rightarrow$ $\angle BAC+\angle DAC=\angle DCA+\angle BCA$

$\Rightarrow$ $\angle BAD=\angle DCB$

Similarly, we can prove, $\angle ADC=\angle ABC$

$\therefore$ We have proved that, opposite angles of a parallelogram are equal.