Question

In the figure, angleA =angle b, angle X=angke Y. Prove that
line ll line n.​

Answer 1

Answer:

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

Hope this is helpful for you.