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 $CE > CF$.

Proof

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Sources

• 1968: M.N. Aref and William Wernick: Problems & Solutions in Euclidean Geometry ... (previous) ... (next): Chapter $1$: Triangles and Polygons: Theorems and Corollaries $1.21 \ \text{(iii)}$