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If two parallel lines are intersected by a transversal ,then what is the sum of interior angles on the same side of the transversal?
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If two parallel lines are intersected by a transversal ,then what is t...

Transversal EF intersects two parallel lines AB and CD at G and H respectively.
To Prove: ∠1 + ∠4 = 180degree and ∠2 + ∠3 = 180degree

Proof: ∠2 + ∠5 = 180degre …equation (i) (Linear pair of angles)
But ∠5 = ∠3 ……………equation (ii) (corresponding angles)
From equations (i) and (ii),
∠2 + ∠3 = 180degree
Also, ∠3 + ∠4 = 180degree ………equation (iii) (Linear pair)
But ∠3 = ∠1 …………..equation (iv) (Alternate interior angles)
From equations (iii) and (iv)
∠1 + ∠4 = 180degree and ∠2 + ∠3 = 180degree Proved
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If two parallel lines are intersected by a transversal ,then what is the sum of interior angles on the same side of the transversal?
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