Question

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Answer 1

Let us assume that

$AB║CD$

EF be the transversal passing through the two parallel lines at$P$and$Q$respectively.

$PR$and $QS$ are the bisectors of $\angle EPB$ and $\angle PQD.$

According to the corresponding angles postulate if a transversal intersects two parallel lines, the corresponding angles will be always equal.

$$\begin{gathered} So,\angle EPB=\angle PQD \\ ½\angle EPB=½\angle PQD \\ \angle EPR=\angle PQS \end{gathered}$$

But, we also know that they are corresponding angles of $PR$ and $QS$

Since the corresponding angles are equal,

We have,

$PR║QS$

Hence Proved.