NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Problems and Solutions

Question 56

Key ideas

• Perpendicular: makes a right angle. Write it as \(90^\circ\).
• Bisector: cuts a segment into two equal parts. It passes through the midpoint. Equal parts are shown by matching tick marks on the segment.
• Perpendicular bisector: does both — it is perpendicular \(\Rightarrow 90^\circ\) and it passes through the midpoint (equal ticks).

Check each figure

1. (i)

   • The line is perpendicular to the segment.
   • No midpoint is shown. There are no equal tick marks on the two halves.
   • Conclusion: only perpendicular is shown.

2. (ii)

   • The line is perpendicular \(\Rightarrow 90^\circ\).
   • It also passes through the midpoint. Tick marks show two equal halves.
   • Conclusion: perpendicular bisector is shown.

3. (iii)

   • The line passes through the midpoint. Tick marks show equal halves.
   • It is not perpendicular. No right angle \(90^\circ\) is shown.
   • Conclusion: only bisector is shown.

Match with the parts in the question

• (a) Perpendicular bisector → (ii)
• (b) Bisector → (ii) and (iii)
• (c) Only bisector → (iii)
• (d) Only perpendicular → (i)