Question

Construct a parallelogram HEAR where HE = 5 cm, EA = 6 cm, and $\angle R={85}^{\circ }$.

Answer 1

Concept :
HEAR is a parallelogram
$\Rightarrow HE=RA=5cm$ and $EA=HR=6cm$ [Since opposite sides of a parallelogram are equal]
Also, $\angle R=\angle E={85}^{\circ }$ [Since opposite angles of a parallelogram are equal]
$\angle H=(180-85{)}^{\circ }={95}^{\circ }$ [Adjacent angles of a parallelogram are supplementry]

Steps of Construction:

1. Draw line segment HE = 5 cm.
2. At E construct an angle of ${85}^{\circ }$. Draw an arc of length 6 cm intersecting the ray from E at A.
3. At A construct an angle of ${95}^{\circ }$. Draw an arc of length 5 cm intersecting the ray from A.
4. With H as centre draw an arc of length 6 cm which intersects the earlier arc. Let it be R.
5. Join HR and AR to complete quadrilateral HEAR.