∠ a≅ ∠ b

To find: line L ∥ line M

Construction: extend C in figure.

∠ a≅ ∠ b (given)

∠ b≅ ∠ c (vertically opposite angle)

∠ a ≅ ∠ c (if whenever an element A is related to an element B and B is related to an element C then A is also related to c that is called transitivity)

But they form a pair of corresponding angle that are congruent.

∴ line L ∥ line M (hence proved).