Question

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel then prove that the two lines are parallel.

Answer 1

given: A transversal AB intersects two lines PQ and RS such that ∠ PLM = ∠ SML

To prove: PQ || RS

Proof: ∠ PLM = ∠ SML (given) ....... (i)

∠ SML = ∠ RMB ....... (ii) (vertically opposite angles)

From equations (i) and (ii),

∠ PLM = ∠ RMB

As these are corresponding angles and corresponding angles equal only if given lines PQ and RS are parallel.

∴ PQ || RS

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