Question

Construct the following quadrilaterals
(i) Quadrilateral $MORE$
$MO=6cm$
$OR=4.5cm$
$\angle M={60}^{\circ }$
$\angle O={105}^{\circ }$
$\angle R={105}^{\circ }$

(ii) Quadrilateral $PLAN$
$PL=4cm$
$LA=6.5cm$
$\angle P={90}^{\circ }$
$\angle A={110}^{\circ }$
$\angle N={85}^{\circ }$

(iii) Parallelogram $HEAR$
$HE=5cm$
$EA=6cm$
$\angle R={85}^{\circ }$

(iv) Rectangle $OKAY$
$OK=7cm$
$KA=5cm$

Answer 1

1)

1. Draw $MO$ of length $6$ cm.

2. Draw an angle of $105$ degree on $O$ and cut an arc of $4.5$ cm on it. The point of intersection is $R$.

3. Draw an angle of $105$ degree on $R$ and draw an angle of $60$ degree on $M$. Their point of intersection is $E$.

4. Join all the points.

$MORE$ is the required quadrilateral.

2)

1. Draw $PL$ of length $4$ cm.

2. Calculate the value of $\angle L$, which comes out to be ${75}^o$.

Draw an angle of ${75}^o$ on $L$ and cut an arc of $6.5$ cm on it. The point of intersection is $A$.

3. Draw an angle of ${110}^o$ on $A$ and draw an angle of ${90}^o$ on $P$. Their point of intersection is $N$.

4. Join all the points.

$PLAN$ is the required quadrilateral.

3)

1. Draw $EA$ of length $6$ cm.

2. Draw an angle of ${85}^o$ on $E$ and cut an arc of $5$ cm on it. The point of intersection is $H$. ($\angle R=\angle E={85}^o$ and $\angle H={95}^o$)

3. Draw an angle of ${95}^o$ on $H$ and cut an arc of $6$ cm. Their point of intersection is $R$.

4. Join all the points.

$HEAR$ is the required parallelogram.

4)

1. Draw $OK$ of length $7$ cm.

2. Draw an angle of ${90}^o$ on $K$ and cut an arc of $5$ cm on it. The point of intersection is $A$.

3. Draw an angle of ${90}^o$ on $A$ and cut an arc of $7$ cm from $A$. The point of intersection is $Y$.

4. Join all the points.

$OKAY$ is the required rectangle.