# NCERT Solutions For Class 6 Maths Practical Geometry Exercise 14.4

**Exercise 14.4**

Ex 14.4 Class 6 Maths Question 1.

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

Solution:

Step I : Draw a line segment (overline { AB }) and mark any point M on it.

Step II : Put the pointer of the compass at M and draw an arc of suitable radius such that it intersects (overline { AB }) at P and Q.

Step III : Take P and Q as centres and radius greater than PM, draw two arcs such that they intersect each other at C.

Step IV : Join M and C.

Thus CM is the perpendicular to (overline { AB }).

Ex 14.4 Class 6 Maths Question 2.

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

Solution:

Step I: Draw a line segment (overline { PQ }) and a point R outside of (overline { PQ }).

Step II : Place a set square on (overline { PQ }) such that one side of its right angle be along it.

Step III: Place a ruler along the longer side of the set square.

Step IV : Hold the ruler fix and slide the set square along the ruler till it touches the point R.

Step V : Join RM along the edge through R. Thus (overline { RM }) ⊥ (overline { PQ }).

Ex 14.4 Class 6 Maths Question 3.

Draw a line l and a point X on it. Through X, draw a line segment (overline { XY }) perpendicular to l. Now draw a perpendicular to (overline { XY }) at y. (Use ruler and compasses)

Solution:

Step I: Draw a line l and take a point X on it.

Step II : Draw an arc with centre X and of suitable radius to intersect the line l at two points P and Q.

Step III : With P and Q as centres and a radius greater than P draw two arcs to intersect each other at M.

Step IV : Join XM and produce to Y.

Step V : With Y as centre and a suitable radius, draw an arc to intersect XY at two points R and S.

Step VI: With R and S as centres and a radius greater than YR, draw two arcs to intersect each other at A.

Step VII: Join Y and A. Thus YA ⊥ XY.

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