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Book I   Proposition 16
Then, since AE is equal to CE, and EB to EF,
    the two sides AE, EB are equal to the two sides CE, EF respectively;
    and the angle AEB is equal to the angle CEF, for they are vertical angles, [I.15]

Therefore
    the base AB is equal to the base FC, and the triangle AEB is equal to the triangle CEF, and the remaining angles are equal to the remaining angles respectively, namely those which the equal sides subtend; [I.4]

therefore
    the angle BAE is equal to the angle ECF.
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