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∠3 + ∠6 = 180
To prove : ‘m’ ∥ ‘n’
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Proof: Clearly, ∠3 + ∠6= 180 (Given)……………………..(1)
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and ∠3 + ∠2= 180 (∵ Linear pair angle)………..(2)
From equation (1) and (2),
∠3 + ∠6 = ∠3 + ∠2
⇒ ∠6 = ∠2
But they are forming a pair of corresponding angles.
‘m’ ∥ ‘n’(By corresponding angles axiom) (Proved)
Theorem 6.5
Lines which are parallel to the same line, are parallel to each other.
Given: ‘l’,‘m’ and ‘n’ are three lines which are cut by a transversal ‘t’.
‘l’ ∥ ‘n’and m’ ∥ ‘n
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