Page 6 - LN

∴ ‘m’ ∥ ‘n’(By corresponding angles axiom) (Proved)

Theorem 6.4

If a transversal intersects two parallel lines, then sum of a pair of co-interior angles is
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supplementary i.e.180 .

Given: ‘m’ ∥ ‘n’and ‘l’ is a transversal.

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To prove : ∠3 + ∠6 = 180

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Proof: Clearly, ∠3 + ∠2 = 180 (Linear pair angle)

⇒ ∠3 + ∠6= 180 (∵ ∠2 = ∠6 , Pair of corresponding angles )
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But they are forming a pair of co-interior angles. (Proved)

Theorem 6.5

If a transversal intersects two lines such that sum of a pair of co-interior angles is
supplementary i.e 180 , then two lines are parallel.
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Given: ‘m’ and ‘n’ are two lines and ‘l’ is a transversal.
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