Question

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 centre an arc FG is drawn (as shown in the figure).

What is the relation between length of arc DM and arc FG?

• A. Length (Arc FG) = 2 $\times$ Length (Arc DM)
• B. Length (Arc FG) = $\frac{1}{2}$ $\times$ Length (Arc DM)
• C. Length (Arc FG) = Length (Arc DM)
• D. Length (Arc FG) = $\frac{3}{2}$ $\times$ Length (Arc DM)

Answer 1

The correct option is C

Length (Arc FG) = Length (Arc DM)

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