Question

Construct a parallelogram $ABCD$, where $AB=7cm,AC=9cm$ and $\angle A={75}^{\circ }$.

Answer 1

In parallelogram sum of adjacent angles are supplementary.

$\therefore$ $\angle A+\angle B={180}^o.$

$\Rightarrow$ ${75}^o+\angle B={180}^o$

$\therefore$ $\angle B={105}^o.$

We know in parallelogram opposite sides and opposite angles are equal.

$\Rightarrow$ Draw a line segment $AB=7cm$

$\Rightarrow$ Take $A$ and $B$ as a center and draw an angle of ${75}^o$ and ${105}^o.$

$\Rightarrow$ Cut off $AC=9,cm$

$\Rightarrow$ Take measure of $BC$ and in compass and cut off $AD$.

$\Rightarrow$ Join $AC,CD,AD.$

$\therefore$ $ABCD$ is a required parallelgram.