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OF Two Triangles which have Two Sides of the one equal to Two Sides of the other, that Triangle which hath the greatest Base hath also the greatest Angle.
Let the Sides AB, DE, AC, DF; of the Triangles ABC, DEF, be equal; and let the Base BC be greater than the Base EF. I say that the Angle A shall be greater than the Angle D.
Demonstration. If the Angle A were not greater than the Angle D, it would be equal, or less; if equal, in
this case the Bases BC would be equal (by the 4th.) If less, then the Base EF would be greater than the Base BC, (by the 24th.) both which is contrary to our Hyp.
These Propositions are of use to De∣monstrate those which follow.