Question

Draw $\angle ABC$ of measure ${60}^{\circ }$ such that $AB=4.5cm$ and $AC=5cm$. Through $C$ draw a line parallel to $AB$ and through $B$ draw a line parallel to $AC$, intersecting each other at $D$. Measure $BD$ and$CD$.

Answer 1

Steps for construction:

$1.$ Draw a line $BX$ and take a point $A$, such that $AB$ is equal to $4.5cm$.
$2.$ Draw $\angle ABP={60}^{\circ }$ with the help of protractor.
$3.$ With $A$ as the centre and a radius of $5cm$, draw an arc cutting $PB$ at $C$.
$4.$ Join $AC$ and $BC$

$5.$ Now, copy $\angle ABP$ and make same angle at centre $C$.

$6.$ Draw a ray $CY$ such that $\angle BCY={60}^{\circ }$, it should be parallel to $AB$. [Since, If lines are parallel then their alternate interior angles are equal.]
$7.$ Similarly copy $\angle CAK$ and make same angle at centre $B$. i.e., $\angle CAK=\angle ABW$ [Since, If lines are parallel then their corresponding angles are equal.]

$8.$ Draw a ray $BW$. it should be parallel to $AC$ and the rays $CY$ , $BW$ intersects at $D$.

Now, measure $BD$ and $CD$, we have:
$BD=5cm=AC$ and $CD=4.5cm=AB$ [Since, $ACDB$ is a parallelogram]