Straight Line making Larger Angle with Perpendicular to Straight Line is Longer

Theorem
Let $AB$ be a straight line.

Let $C$ be a point which is not on $AB$.

Let $D$ be a point on $AB$ such that $CD$ is perpendicular to $AB$.

Let $E, F$ be points on $AB$ such that $\angle DCE > \angle DCF$.

Then $CE > CF$.