A transversal intersects two parallel lines.


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


Given Two lines AB and CD are parallel and intersected by transversal t at P and 0, respectively. Also, EP and FQ are the bisectors of angles ∠APG and  ∠CQP, respectively.

To prove $E P \| F Q$

Proof Given, $A B \| C D$

$\Rightarrow \quad \angle A P G=\angle C Q P$ [corresponding angles]

$\Rightarrow$ $\frac{1}{2} \angle A P G=\frac{1}{2} \angle C Q P$ [dividing both sides by 2]

 $\Rightarrow$ $\angle E P G=\angle F Q P$

$[\because E P$ and $F Q$ are the bisectors of $\angle A P G$ and $\angle C Q P$, respectively]

As these, are the corresponding angles on the transversal line $t$.

$\therefore \quad E P \| F Q$ 

Hence proved.


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