Question

Draw a line segment PQ = 8 centimeter. Construct a perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meet PQ at point R. Measure the length of PR and QR. Is PR = QR?

Answer 1

Hint: Firstly we will draw a line segment of 8 cm. Then taking the endpoints of the centre, we will draw an arc on both sides with equal radii by taking radii of more than half of length of PQ. And then we will mark those arcs. And, lastly we will join point RS.

Complete step-by-step answer:
Before solving this question, we must know the difference between Constructing and Drawing in mathematics.
There is a difference between constructing and drawing.
To CONSTRUCT something means to use compasses and scale.
To DRAW something means to use a protractor or just a scale.
To solve this question, we will have to follow some steps, which are mentioned in detail below, in the solution. Here is a short explanation:-
We will firstly have to draw a line of 8 cm. Then we will draw arcs on both the sides of the line. Then we will join the two arcs. And hence, we will get the perpendicular bisector of the line segment.

Steps of Construction: 
1. Draw a line segment PQ of 8 centimeter.

2. With P and Q as centers, draw arcs on both sides of PQ with equal radii. The radius should be more than half the length of PQ. 
3. Let these arcs cut each other at points R and S. 
4. Join RS which cuts PQ at O. Then RS=PQ. Also ∠POR=$90^0$.

Hence, the line segment RS is the perpendicular bisector of PQ as it bisects PQ. On measuring the lengths of PR=4cm, QR=4 cm Since PR=QR, both are 4cm each. ∵ PR = QR.

Note: Doing such questions using scales and protractors to make perpendiculars, angles, etc. would be wrong. It is always mentioned in the question that whether one needs to construct or draw a perpendicular/angle so, students must read the question very carefully. Diagram must be neat and clean.