Two Intersecting Straight Lines are in One Plane

Proof

 * Euclid-XI-2.png

Let the two straight lines $AB$ and $CD$ intersect at the point $E$.

Let $F$ and $G$ be arbitrary points on $EC$ and $EB$.

Let $CB$ and $FG$ be connected.

Let $FH$ and $GK$ be drawn across.

Suppose part of $\triangle ECB$ is in the plane of reference and the rest of it in another plane.

Then a part of one of the straight lines $EC$ and $EB$ will be in the plane of reference and the result in another plane.

But from, this cannot happen.

Therefore $\triangle ECB$ is all in one plane.

But whatever plane $\triangle ECB$ is in, each of the straight lines $EC$ and $EB$ are also in that plane.

And in whatever plane $EC$ and $EB$ are in, the straight lines $AB$ and $CD$ are also in that plane.

Therefore $AB$ and $CD$ are in one plane, and every triangle is in one plane.