Problem
When a straight line $XY$ is perpendicular to $CD$ of the parallel lines $AB$ and $CD$, it is also perpendicular to the other $AB$.
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Solution
Since $AB$ and $CD$ are parallel, the straight line $XY$ that intersects $CD$ at the point $F$ also intersects $AB$.
If this point of intersection is $E$, the corresponding angles $∠AEX$ and $∠CFE$ are equal.
Then,
$$∠CFE=∠R,$$
$$∴ \ ∠AEX=∠R,$$
$$∴ \ AB⊥XY.$$
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Reference
Teiichiro Sasabe (1976) The Encyclopedia of Geometry (2nd edition), Seikyo-Shinsha, p.7