Two Straight Lines make Equal Opposite Angles/Porism

Porism to Two Straight Lines make Equal Opposite Angles

It follows that if two straight lines cut one another, the angles at the point of intersection make four right angles.

In the words of Euclid:

From this it is manifest that, if two straight lines cut one another, they will make the angles at the point of section equal to four right angles.

(The Elements: Book $\text{I}$: Proposition $15$ : Porism)

Proof

Follows directly from:

Proposition $13$ of Book $\text{1} $: Two Angles on Straight Line make Two Right Angles

and:

Proposition $15$ of Book $\text{1} $: Two Straight Lines make Equal Opposite Angles

Sources

• 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 1 (2nd ed.) ... (previous) ... (next): Book $\text{I}$. Propositions