Problem
“If there are straight lines $A’O’$ and $B’O’$ that both pass through point $O’$, and $A’O’$ and $B’O’$ are respectively perpendicular to straight lines $AO$ and $BO$ that both pass through point $O$, then $∠AOB$ and $∠A’O’B’$ are equal.” Is this proposition correct?
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Solution
It is wrong.
As shown in the figure, $∠AOB$ and ∠$A’O’B’$ may form complementary angles.
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Reference
Teiichiro Sasabe (1976) The Encyclopedia of Geometry (2nd edition), Seikyo-Shinsha, pp.5-6