Start by noticing that ∠ 1 and ∠ 4 form a as well as ∠ 2 and ∠ 3.
Therefore, these pair of angles are supplementary.
m∠ 1 + m∠ 4 = 180^(∘) & (I) m∠ 2 + m∠ 3 = 180^(∘) & (II)
On the other hand, since the lines l_1 and l_2 are parallel, by the , the are . This allows to write the following relations.
∠ 1 ≅ ∠ 3 & ⇒ m∠ 1 = m∠ 3 [0.25em]
∠ 2 ≅ ∠ 4 & ⇒ m∠ 2 = m∠ 4
Next, in Equation I, substitute m∠ 2 for m∠ 4.
m∠ 1 + m∠ 4 = 180^(∘)
m∠ 1 + m∠ 2 = 180^(∘)
The last implies that ∠ 1 and ∠ 2 are supplementary. Similarly, in Equation II, substitute m∠ 4 for m∠ 2.
m∠ 2 + m∠ 3 = 180^(∘)
m∠ 4 + m∠ 3 = 180^(∘)
As before, the last equation implies that ∠ 3 and ∠ 4 are supplementary, which completes the proof.
