Question

Question 3
A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Answer 1

Given, two lines AB and CD are parallel and intersected by transversal t at P and Q respectively. Also, EP and FQ are the bisectors of angles $\angle APGand\angle CQP$, respectively.

To prove: EP||FQ
Proof:
Given, AB || CD.
$\Rightarrow \angle APG=\angle CQP$ [corresponding angles]
$\Rightarrow \frac{1}{2}\angle APG=\frac{1}{2}\angle CQP$ [dividing both sides by 2]
$\Rightarrow \angle EPG=\angle FQP$
[$\because$ EP and FQ are the bisectors of $\angle APGand\angle CQP$ respectively]
These are the corresponding angles on the transversal line t.
$\therefore$ EP || F Q
Hence, proved.