Haryana State Board HBSE 6th Class Maths Solutions Chapter 14 Practical Geometry Ex 14.4 Textbook Exercise Questions and Answers.

## Haryana Board 6th Class Maths Solutions Chapter 14 Practical Geometry Exercise

## 14.4

Question 1.

Draw any line \(\overleftrightarrow{\mathrm{AB}}\) . Make any point M on it. Through M draw a

perpendicular to \(\overleftrightarrow{\mathrm{AB}}\) . (Use Ruler and compasses).

Solution:

(i.) With M as centre and a convenient radius, draw an arc intersecting the line \(\overleftrightarrow{\mathrm{AB}}\) at two points C and D.

(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 [Fig.].

Question 2.

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

Soution:

(i) Place a set-square on \(\overleftrightarrow{\mathrm{PQ}}\) such that one arm of its right-angle aligns along \(\overleftrightarrow{\mathrm{PQ}}\) .

(ii) Place a ruler along the edge opposite to the right-angle of the set- P 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 \(\overleftrightarrow{\mathrm{PQ}}\) at M. Then, RM ⊥ PQ.

Question 3.

Draw a line T and a point X on it. Through X, draw a line \(\overleftrightarrow{\mathrm{XY}}\) perpendi¬cular to Z. Now, draw a perpendicular to \(\overleftrightarrow{\mathrm{XY}}\) at Y. (Use ruler and compasses).

Solution:

(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 XC 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 a radius greater than YD, draw two arcs, which cut each other at F.

(vii) Join YF, then YF is perpendicular to XY at Y.