Question

Construct $\Delta DEF$ such that $m\angle DFE={120}^o,DE=8.5$ cm, seg $FK$ is the median and length of $FK=3$ cm.

Answer 1

1. Draw base $DE$ of length $8.5cm$. Draw perpendicular bisector of $DE$ and mark the midpoint as $K$.

2. Draw an angle of ${120}^{\circ }-{90}^{\circ }={30}^{\circ }$ from poin $D$ and let it intersect the perpendicular bisector at $O$.

3. With centre as $O$ and $DO$ as radius, draw a circle which passes through $D$ and $E$.

4. With one end of compass at $K$ and radius as $FK=3cm$, draw an arc and let it intersect the circle at $F$.

$\Delta DEF$ is the required triangle.