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

Answer 2

given: A transversal AB intersects two lines PQ and RS such that ∠ PLM = ∠ SMLTo prove: PQ || RSProof: ∠ PLM = ∠ SML (given) ....... (i)∠ SML = ∠ RMB ....... (ii) (vertically opposite angles)From equations (i) and (ii),∠ PLM = ∠ RMBAs these are corresponding angles and corresponding angles equal only if given lines PQ and RS are parallel.∴ PQ || RS