Class 6 - Mathematics : Practical Geometry
Exercise : 14.4
Top Block 1
NCERT Solutions Class 6 Mathematics Practical Geometry Ex 14.4
Question: 1.Draw any line segment AB. Mark any point M on it. Through M, draw a perpendicular to AB. (Use ruler and compasses)
Answer :
Steps of construction:
(i) With M as centre and a convenient radius, draw an arc intersecting the line AB at two points C and B.
(ii) With C and D as centres and a radius greater than MC, draw two arcs, which cut each other at P.
(iii) Join PM. Then PM is perpendicular to AB through the point M.
(ii) With C and D as centres and a radius greater than MC, draw two arcs, which cut each other at P.
(iii) Join PM. Then PM is perpendicular to AB through the point M.
Question: 2.Draw any line segment PQ. Take any point R not on it. Through R, draw a perpendicular to PQ. (Use ruler and set-square)
Answer :
Steps of construction:
Mddle block 1
(i) Place a set-square on 
such that one arm of its right angle aligns along .
(ii) Place a ruler along the edge opposite to the right angle of the set-square.
(iii) Hold the ruler fixed. Slide the set square along the ruler till the point R touches the other arm of the set square.
(iv) Join RM along the edge through R meeting
at M. Then RM ⊥ PQ.
such that one arm of its right angle aligns along .(ii) Place a ruler along the edge opposite to the right angle of the set-square.
(iii) Hold the ruler fixed. Slide the set square along the ruler till the point R touches the other arm of the set square.
(iv) Join RM along the edge through R meeting
at M. Then RM ⊥ PQ.
Question: 3.Draw a line l and a point X on it. Through X, draw a line segment XY perpendicular to l. Now draw a perpendicular to XY to Y. (use ruler and compasses)
Answer :
Steps of construction:
(i) Draw a line ′l′ and take point X on it.
(ii) With X as centre and a convenient radius, draw an arc intersecting the line ′l′ at two points A and B.
(iii) With A and B as centres and a radius greater than XA, draw two arcs, which cut each other at C.
(iv) Join AC and produce it to Y. Then XY is perpendicular to ′l′.
(v) With D as centre and a convenient radius, draw an arc intersecting XY at two points C and D.
(vi) With C and D as centres and radius greater than YD, draw two arcs which cut each other at F.
(vii) Join YF, then YF is perpendicular to XY at Y.
(ii) With X as centre and a convenient radius, draw an arc intersecting the line ′l′ at two points A and B.
(iii) With A and B as centres and a radius greater than XA, draw two arcs, which cut each other at C.
(iv) Join AC and produce it to Y. Then XY is perpendicular to ′l′.
(v) With D as centre and a convenient radius, draw an arc intersecting XY at two points C and D.
(vi) With C and D as centres and radius greater than YD, draw two arcs which cut each other at F.
(vii) Join YF, then YF is perpendicular to XY at Y.