Page 5 - LN

Given:‘m’ ∥ ‘n’

To prove : ∠3 = ∠5

Proof: Clearly, ∠1 = ∠5 (By corresponding angle axiom)

⇒ ∠3 = ∠5 (∵ ∠1 = ∠3 , Vertically Opposite angles)

But they are forming a pair of alternate angles. (Proved)

Theorem 6.3

If a transversal intersects two lines such that a pair of alternate angles is equal, then the
two lines are parallel.

Given: ‘m’ and ‘n’ are two lines which are cut by transversal ‘l’ .

and ∠3 = ∠5

To prove : ‘m’ ∥ ‘n’

Proof: Clearly, ∠3 = ∠5 (Given)

⇒ ∠1 = ∠5 (∵ ∠1 = ∠3 , Vertically Opposite angles)

But they are forming a pair of corresponding angles.
5