Question

(a) Draw a line l. Draw a perpendicular on l at any point. On this perpendicular, choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

(b) Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as the centre an arc FG is drawn (as shown in the figure).

What is the relation between the length of arc DM and arc FG?
[4 MARKS]

Answer 1

Each part: 2 Marks

(a) To construct: A line parallel to given line when the perpendicular line is also given.


Draw a line l and take a point P on it.

At point P, draw a perpendicular line n.

Take PX = 4 cm on line n.

At point X, again draw the line m.

(b) Since both the angles are alternate interior angles, they will be equal to each other. Also, since both arcs are drawn with the same radius, they are part of two equal circles. This means that they both have same shape and size. Thus, the two arcs DM and FG are congruent which makes their lengths equal.