Question

Construct a $\Delta PQR$ in which QR = 6cm, PQ = 4.4 cm and PR = 5.3 cm. Draw the bisector of $\angle P$.

Answer 1

Hint: We will first draw the baseline of 6cm and with the help of compass we will cut an arc from one point of line at 4.4cm and again cut the arc from the other side at 5.3cm. Join the line to get the required triangle. Finally form the angle bisector at angle P.

Complete step by step answer:
It is given in the question that we have to construct a triangle PQR in which QR is 6cm, PQ is 4.4cm and PR is 5.3cm. Also, we have to construct the angle bisector of angle P.
Instruments required to form the triangle and angle bisector are:
(1) Pencil
(2) Scale
(3) Compass
(4) Eraser
We will construct the required triangle step by step.
Step 1. First we will construct a baseline QR = 6cm.

Step 2. We will take 4.4cm in the compass and cut an arc at 4.4cm from point Q.

Step 3. We will take 5.3cm on the compass and then we will cut an arc at 5.3cm from point R. We will get the intersection point of both arcs as a point named P.

Step 4. Now, we will join point Q with point P and we will get side PQ = 4.4cm and similarly we will join point R with point P and we will get side RP = 5.3cm.

Now, we get a triangle PQR, in which side PQ = 6cm, PR = 4.4cm and side QP = 5.3cm.
Step 5. Now, we will construct the angle bisector at $\angle P$.
Construction of an angle bisector at $\angle P$ is as follows.
We will cut an arc from point A and then we will cut the second arc from point B. Then from the point of intersection of two arcs and the point P we will draw a straight line and the $\angle P$ is bisected.

So, as of now we are ready with our required triangle PQR in which side QR = 6cm, side PQ = 4.4cm and side PR = 5.3cm. Also, we have constructed the angle bisector of angle P.

Note: Please use the instrument for construction and go step by step to get the final result. In the construction of the angle bisector place the compass at one side of the angle and cut the first arc. Similarly, put the compass at the second end and cut the second arc. The point where the both arcs intersect must be darkened and then we can draw a line from that dark point to the angle we want to bisect.
Example: We want to bisect angle CAB. So, we cut an arc from point D and the point E finally draw a line passing through the intersection point and angle CAB.