Q175Short answer
A line l is parallel to line m and a transversal p interesects them at X, Y respectively. Bisectors of interior angles at X and Y interesct at P and Q. Is PXQY a rectangle? Given reason.
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l ∠DXY = ∠XYA (alt int. ∠S) ∠DXY ∠XYA = (÷2) 2 2 ∠1 = ∠2 (XP and YQ are bisectors) QY ∴ XP (1) PY Similarly XQ (2) From (1) and (2) PXQY is a parallelogram ∠DXY + ∠XYB = 1800 ∠DXY ∠XYB 1800 + = (÷ by 2) 2 2 2 ∠1 + ∠3 = 900 (4) In ∆XYP ∠1 + ∠3 + ∠P = 1800 900 + ∠P = 1800 (from 4) ∠P = 900 From (3) and (5), PXQY is a rectangle