RBSE Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.4

Rajasthan Board RBSE Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.4 Textbook Exercise Questions and Answers.

RBSE Class 6 Maths Solutions Chapter 14 Practical Geometry Ex 14.4

Question 1.
Draw any line segment \(\overline{A B}\). Mark any point M on it. Through M, draw a perpendicular to AB (use ruler and compasses). 
Answer:
Steps of construction :

1. Draw a line segment AB and mark a point M on it.
2. Keep needle of the compass at M draw an arc such that it intersect \(\overline{A B}\) at P and Q.
3. Now take an arc of any radius, put the needle of the compass at P and cut an arc upward.
4. Again put the needle of the compass at Q and cut an arc of same radius in upward direction.
5. Let these arcs intersect each other at point C.
6. Join C and M.

Thus, CM is perpendicular to AB.

Question 2.
Draw any line segment \(\overline{P Q}\). Take any point R not on it. Through R, draw a perpendicular to \overline{P Q} (Use set square and ruler).
Answer:
Construction method :
1. Draw a line segment \(\overline{P Q}\) and take a point R outside it.  
2. Place a set square on \(\overline{P Q}\) such that one arm of its right angle aligns along \(\overline{P Q}\).
3. Now place a ruler along the edge opposite to right angle of the set square.

4. Hold the ruler fixed. Slide the set square along the ruler till the point R touches the other arm of the set square.
5. Join RM along the edge through R.
Now \(\overline{R M}\) ⊥ \(\overline{P Q}\)

Question 3.
Draw a line l and a point X on it. Through X, draw a line segment \(\overline{X Y}\) perpendicular to l. Now draw a perpendicular to \(\overline{X Y}\) at Y (Use ruler and compasses).
Answer:
Steps of construction :
(1) Make a fine T and take point X on it.
(2) With X as centre and a certain radius, cut an arc to intersect the line T at 2 points P and Q.
(3) With P and Q as centres and a radius greater than XP, draw 2 arcs, which cut each other at M.
(4) Join X and M and produce it to Y. Then XM is perpendicular to T.

(5) With Y as centre and certain radius, draw an arc intersecting \(\overline{X Y}\) at two points R and S.
(6) With R and S as centres and radius greater then YR, draw 2 arcs and they cut each other at N.
(7) Join Y and N.
Thus, YN is perpendicular to XY at Y.