Problem
Two straight lines perpendicular to the same straight line are parallel to each other.
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Solution
Assume that $AB$ and $CD$ are both orthogonal to $XY$ at $A$ and $C$, and that $B$ and $D$ are both on the same side of $XY$.
Then,
$$AB⊥XY,$$
$$∴ \ ∠BAY=∠R.$$
$$CD⊥XY,$$
$$∴ \ ∠DCY=∠R.$$
Therefore, since the corresponding angles are equal,
$$AB∥CD.$$
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Reference
Teiichiro Sasabe (1976) The Encyclopedia of Geometry (2nd edition), Seikyo-Shinsha, p.7