|Book I Proposition 45|
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];
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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