T
H
E

E
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M
E
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Book I   Proposition 45
Then, since
    each to the angles FKH, GHM is equal to the angle E,
    the angle FKH is also equal to the angle GHM. [C.N.1]

    Let the angle KHG be added to each;
therefore the angles FKH, KHG are equal to the angles KHG, GHM.
    But the angles FKH, KHG are equal to two right angles [I.29];
therefore
    the angles KHG, GHM are also equal to two right angles.

    Thus, with a straight line GH, and at a point H on it, two straight lines KH, HM not lying on the same side make adjacent angles equal to two right angles; therefore
    KH is in a straight line with HM. [I.14]
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