GSEB Class 6 Maths Solutions Chapter 14 Practical Geometry Exercise 14.4

Question 1. Draw any line segment \( \overline{\mathrm{AB}} \). Mark any point M on it. Through M, draw a perpendicular to \( \overline{\mathrm{AB}} \) (Use ruler and compasses)
Answer:
Steps of construction:
Step I: First, draw a line piece \( \overline{\mathrm{AB}} \) and put a point M on it.
Step II: Next, place the compass's metal tip at M and open it to a helpful width. Draw an arc so it crosses line AB at points P and Q.
Step III: Then, using P and Q as middle points, and a distance bigger than PM, draw two arcs that cross each other at C.
Step IV: Finally, connect C and M. This way, line CM is perpendicular to AB.

Exam Tip: For geometry construction questions, always list the steps clearly and label the diagram accurately to score full marks.

Question 2. Draw any line segment \( \overline{\mathrm{PQ}} \). Take any point R, not on it. Through R, draw a perpendicular to \( \overline{\mathrm{PQ}} \). (Use ruler and set-square)
Answer:
Steps of construction:
Step I: First, draw a line segment \( \overline{\mathrm{PQ}} \) and pick a point R that is not on it.
Step II: Next, put a set-square on line \( \overline{\mathrm{PQ}} \) so that one side of its right angle sits along it.
Step III: Then, place a ruler next to the side of the set-square that is opposite its right angle.
Step IV: Keep the ruler steady and slide the set-square along it until point R meets the other side of the set-square.
Step V: Finally, draw a line connecting R and M along the set-square's edge, which meets the line piece PQ at M. So, \( \overline{\mathrm{RM}} \) is perpendicular to PQ.

Exam Tip: When using a set-square, make sure the ruler is held firmly to ensure accurate parallel movement and precise perpendicular lines.

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 at Y. (Use ruler and compasses)
Answer:
Steps of construction:
Step I: First, draw a line 'l' and mark a point X on it.
Step II: Next, with X as the middle point and a good radius, draw an arc that cuts line 'l' at two points, P and Q.
Step III: Then, with P and Q as centres and a radius larger than PX, draw two arcs that cross each other at M.
Step IV: Connect X and M, and extend this line to Y. This means XY is perpendicular to line l.
Step V: Using Y as the middle and a suitable radius, draw an arc that cuts XY at two points, R and S.
Step VI: Then, with R and S as centres and a radius bigger than YR, draw two arcs that cross each other at 'N'.
Step VII: Finally, connect Y and N. So, line YN is perpendicular to XY at point Y.

Exam Tip: When drawing a perpendicular at a point on a line, ensure your arcs have a radius greater than the distance from the point to the intersecting arc points for accurate intersection.