The theorem on the sum of one-sided angles formed at the intersection of two parallel and secant.

Let’s remember and prove the theorem on the sum of one-sided angles formed at the intersection of two parallel and secant.

It sounds like this:

If two parallel lines are intersected by a secant, then the sum of the one-sided angles is 180 °.

Proof:

Let m and n be two parallel lines that are intersected by the secant l.

Let’s prove that ∠ 1 + ∠ 4 = 180 °.

∠ 1 = ∠ 2, since the lines m || n. ∠ 2 and 4 are adjacent and add up to 180 °.

Since ∠ 1 = ∠ 2 and ∠ 2 + ∠ 4 = 180 °, we conclude that ∠ 1 + ∠ 4 = 180 °.

Q.E.D.