Theorem – Same side of the transversal, Angles are Supplementary

If a transversal intersect two parallel lines, then each pair of interior angles on the Same side of the transversal are Supplementary.

Given: Two parallel Lines AB and CD, and PS be transversal intersecting AB at Q and CD at R.

To Prove: Sum of interior angles on the Same side of the transversal is Supplementary.

i.e.  ∠AQR + ∠CRQ = 1800 and ∠BQR + ∠DRQ = 1800

Proof: Parallel lines AB and CD, and PS be transversal
intersecting AB at Q and CD at R.

So that, ∠AQP = ∠CRQ (Corresponding angles)…1

For line PS 

∠AQP + ∠AQR = 1800  (Linear pair)….2

Putting the value of (1) in (2)

∠AQR + ∠CRQ = 1800

Similarly we can prove that

∠BQR + ∠DRQ = 1800

Therefore, sum of interior angles on same side of transversal is 1800 .

                                           Hence proved.

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