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Question
A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.
Solution
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 ∠APG and ∠CQP, respectively.
To prove: EP || FQ
Proof: Given, AB || CD
⇒ ∠APG = ∠CQP ...[Corresponding angles]
⇒ `1/2 ∠APG = 1/2 ∠CQP` ...[Dividing both sides by 2]
⇒ ∠EPG = ∠FQP ...[∵ EP and FQ are the bisectors of ∠APG and ∠CQP, respectively]
As these, are the corresponding angles on the transversal line t.
∴ EP || FQ
Hence proved.
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