Question

(i) If a transversal intersects two parallel lines then state the relation between alternate angles.
(ii) If each of the two parallel lines are parallel to the third line then what is the relation between them?
(iii) If a transversal intersects two parallel lines and the corresponding sides of two angles are parallel then what is the relation between these angles?
(iv) If AB is a line and P is a point outside it then how many lines can be drawn through P and Parallel to AB?
(v) If a transversal intersects two parallel lines such that the ratio between the interior angles on one of its side is 2:7, then find the measure of the greater angle.

Answer 1

(i)


Here, l and m are the parallel lines and t is the transversal.
Thus, the alternate angles are equal or congruent.

(ii)


We have:
$$\begin{gathered} l\parallel n\mathrm{and}m\parallel n \\ \therefore l\parallel m \end{gathered}$$

(iii)



The corresponding angles are equal or congruent.



According to the figure, only one line can be drawn parallel to AB through P.

(v)

Let the angles be multiples of x.
Then one angle = 2x
and other angle = 7x
We know that the interior angles on the same side of the transversal are supplementary.
Thus, 2x + 7x = 180^o
⇒ 9x = 180^o
⇒ x =20^o
∴ Greater angle = 7 $\times$ 20^o = 140^o