Opposite Sides Form Anti-Parallel Lines

What are antiparallel lines?

Now, consider the following diagram :

(The equal angles are highlighted in the same colour)

They're similar because they have 2 angles that have the same measure.

Why did I tell you about this when I'm suppose to talk about antiparallel lines? They're actually quite similar. Consider the following diagram :

$ABC$ is a triangle. Let $E$ be a point on $AC$. The circumcircle of $BCE$ intersect $AB$ at $D$. $DE$ (marked in yellow) and $BC$ (marked in cyan) are called antiparallel.

Again, $\triangle ADE \sim \triangle ABC$.

Note that $DE$ in the second diagram is the same as $DE$ in the first diagram reflected about the angle bisector of $\angle A$.

Thus, we arrive at the definition :

Given a line $n$, we say that $l$ and $m$ (both not parallel to $n$) are antiparallel with respect to $n$ if the reflection of $l'$ of $l$ about $n$ is parallel to $m$. Often, if the line $n$ is clear in the context, we often just say that $l$ is antiparallel to $m$.