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Book IV   Proposition 9
Now, since DA is equal to AB, and AC is common, therefore
    the two sides DA, AC are equal to the two sides BA, AC; and the base DE is equal to the base BC;
therefore
    the angle DAC is equal to the angle BAC. [I.8]
Therefore
    the angle DAB is bisected by AC.

Similarly
    we can prove that each of the angles ABC, BCD, CAD is bisected by the straight lines AC, DB.
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