NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions

Question 48

Step-by-step explanation (very easy)

We want to bisect a line segment. Bisect means “cut into two equal parts”.

What you need

• A ruler (straightedge without markings is fine)
• A compass
• A pencil

Construction steps

1. Draw the segment.

   Draw the line segment (AB).

2. Open the compass.

   Place the compass point on (A). Open it a little more than half of (AB). (No need to measure exactly — just make sure it’s bigger than half.)

3. Make two arcs from (A).

   With center (A), draw an arc above the segment.

   With the same opening, draw an arc below the segment.

4. Make two arcs from (B).

   Without changing the compass width, place the point on (B).

   Draw an arc above the segment to cross the first arc.

   Draw an arc below the segment to cross the other arc.

5. Mark the intersection points.

   Let the arcs meet above at (P).

   Let the arcs meet below at (Q).

6. Draw the bisector line.

   Use the ruler to draw a straight line through points (P) and (Q). This line will cut segment (AB).

7. Mark the midpoint.

   Let the line (PQ) meet (AB) at (M).

   Point (M) is the midpoint of (AB).

Why this works (simple reason)

The arcs were drawn with the same compass width from (A) and from (B). So the crossing points (P) and (Q) are equally far from (A) and (B).

If two points are equally far from (A) and (B), then the line through those points is the perpendicular bisector of (AB). That means it cuts (AB) into two equal parts and is at right angles to it.

Conclusion

With a ruler and compasses, we can always bisect any given line segment.