These NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.4 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.4

Question 1.

Draw any line segment \(\overline{\mathrm{AB}}\). Mark any point M on it. Through M, draw a perpendicular to \(\overline{\mathrm{AB}}\). (Use ruler and compasses)

Answer:

Steps of construction:

- With M as centre and a convenient radius, draw an arc intersecting the line AB at two points C and B.
- With C and D as centres and a radius greater than MC, draw two arcs, which cut each other at P.
- Join PM. Then PM is perpendicular to AB through the point M.

Question 2.

Draw any line segment \(\overline{\mathrm{PQ}}\). Take any point R not on it. Through R, draw a perpendicular to \(\overline{\mathrm{PQ}}\). (Use ruler and set- square)

Answer:

Steps of construction:

- Place a set-square on \(\overline{\mathrm{PQ}}\) such that one arm of its right angle aligns along \(\overline{\mathrm{PQ}}\).
- Place a ruler along the edge opposite to the right angle of the set-square.
- Hold the ruler fixed. Slide the set square along the ruler till the point R touches the other arm of the set square.

- Join RM along the edge through R meeting \(\overline{\mathrm{PQ}}\) at M. Then RM ⊥ PQ.

Question 3.

Draw a line 1 and a point X on it. Through X,draw a line segment \(\overline{\mathrm{XY}}\) perpendicular to 1. Now draw a perpendicular to \(\overline{\mathrm{XY}}\) to Y. (use ruler and compasses)

Answer:

Steps of construction:

- Draw a line ’l’ and take point X on it.
- With X as centre and a convenient radius, draw an arc intersecting the line ’l’ at two points A and B.
- With A and B as centres and a radius greater than XA, draw two arcs, which cut each other at C.
- Join AC and produce it to Y. Then XY is perpendicular to ’l’
- With D as centre and a convenient radius, draw an arc intersecting XY at two points C and D.
- With C and D as centres and radius greater than YD, draw two arcs which cut each other at F.
- Join YF, then YF is perpendicular to XY at Y.