## The Theorem

The two interior angles formed by a transversal line intersecting two parallel lines are supplementary (i.e: sum up to 180°).

## The problem

AB||CD, prove m∠5 + m∠4 = 180°

So how do we go about this? We already know that the 2 angles that are next to each other and which form a straight line are “Supplementary angles” and their sum is 180°. So we will try to use that since here we also need to prove that the sum of two angles is 180°.

So let’s proceed to the proof, using what we already know about

## Proof

(1) AB||CD //given

(2) ∠1 ≅ ∠5 //from the axiom of parallel lines – corresponding angles

(3) m∠1 = m∠5 //definition of congruent angles

(4) m∠1 + m∠4 = 180° // straight line measures 180°

(5) m∠5 + m∠4 = 180° //using (3) and performing algebraic substitution, replacing m∠1 with the equivalent m∠5

And we have proven the theorem.