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In Euclid's The Elements, Book 1, Proposition 4, he makes the assumption that one can create an angle between two lines and then construct the same angle from two different lines. I do not see anywhere in the list of definitions, common notions, or postulates that allows for this assumption. When teaching my students this, I do teach them congruent angle construction (with straight edge and compass), but do not understand why Euclid is allowed to make this logical leap. Thanks for any help you can give.

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    $\begingroup$ This question doesn't belong on Mathoverflow, but might get a good reception on matheducators.stackexchange.com $\endgroup$
    – David E Speyer
    Commented Jan 29, 2020 at 1:46
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    $\begingroup$ Posted on MESE here. $\endgroup$
    – Joseph O'Rourke
    Commented Jan 29, 2020 at 14:01

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