Question

In the following figure, show that

1. AB || CD
2. EF || GH

Answer 1

We have,

1. ∠PSC = ∠RSF = 50° ...[Vertically opposite angles]
   ∠APS + ∠PSC = 130° + 50° = 180°
   As ∠APS and ∠PSC are interior angles on the same side of transversal EF and are supplementary.
   ∴ AB || CD.
2. ∠APS = ∠EPQ = 130° ...[Vertically opposite angles]
   ∠EPQ + ∠GQP = 130° + 50° = 180°
   As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary.
   ∴ EF || GH.