Question

Draw $\Delta PQR$ in which $PQ=3cm$, $QR=4cm$, and $RP=5cm$. Also draw the bisector of $\angle Q$ .

Answer 1

Steps of construction:

1. Draw a line segment $PQ$ of length $3cm$.
2. With $Q$ as centre and radius $4cm$, draw an arc.
3. With $P$ as centre and radius $5cm$, draw an arc intersecting the previously drawn arc at $R$.
4. Join $PR$ and $QR$ to obtain the required triangle.
5. From $Q$, cut arcs of equal radius intersecting $PQ$ and $QR$ at $M$ and $N$, respectively.
6. From $M$ and $N$, cut arcs of equal radius intersecting at point $S$.
7. Join $QS$ and extend to produce the angle bisector of angle $PQR$ whose measure is ${90}^{\circ }$.
8. Verify that angle $PQS$ and angle $SQR$ are equal to ${45}^{\circ }$ each.