# HBSE 6th Class Maths Solutions Chapter 14 Practical Geometry Ex 14.4

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

## 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.