Question

In the given figure, if ∠a ≅ ∠b and ∠x ≅ ∠y then prove that line l || line n.

Answer 1

We have ∠a ≅ ∠b 

⇒ m∠a = m∠b

But ∠a and ∠b are corresponding angles formed by a transversal k of line m and line l. 

∴ line m || line l       ...(corresponding angles test)

Also, we have ∠x ≅ ∠y 

⇒ m∠x = m∠y

But ∠x and ∠y are alternate interior angles formed by a transversal k of line m and line n. 

∴ line m || line n      ...(alternate angles test)

So, we have line m || line l and line m || line n.

It is known that if two lines in a plane are parallel to a third line in the plane, then those two lines are parallel to each other.

∴ line l || line n