## Chapter 2 Parallel Lines and Transversals Set 2.3

Question 1.

Draw a line l. Take a point A outside the line. Through point A draw a line parallel to line l.

Solution:

Steps of construction:

- Draw a line l and take any point A outside the line.
- Place a set-square, such that one arm of the right angle passes through A and the other arm is on line l.
- Place the second set-square as shown in the figure such that the vertex of the right angle is at point A.
- Hold the two set-squares in place and draw a line parallel to line l through the edge of the second set-square. Name the line as m.

Line m is the required line parallel to line l and passing through point A.

Question 2.

Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line l.

Solution:

Steps of construction:

- Draw a line l and take any point T outside the line.
- Place a set-square, such that one arm of the right angle passes through T and the other arm is on line l.
- Place the second set-square as shown in the figure such that the vertex of the right angle is at point T.
- Hold the two set-squares in place and draw a line parallel to line l through the edge of the second set-square. Name the line as m.

Line m is the required line parallel to line l and passing through point T.

Question 3.

Draw a line m. Draw a line n which is parallel to line m at a distance of 4 cm from it.

Solution:

Steps of construction:

- Draw a line m and take any two points M and N on the line.
- Draw perpendiculars to line m at points M and N.
- On the perpendicular lines take points S and T at a distance 4 cm from points M and N respectively.
- Draw a line through points S and T. Name the line as n.

Line n is parallel to line m at a distance of 4 cm from it.