On Propositions I.4 through I.8
This next group of propositions includes two congruence propositions for triangles, I.4 and I.8, and two propositions about isosceles triangles, I.5 and I.6. Proposition I.7 is only used in I.8 and could have been made part of I.8, but was probably separated in order to reduce the length of the proof in I.8.
Proposition I.4
This is the familiar side-angle-side congruence proposition. When two triangles have two sides and the included angle equal, then the remaining sides, angle, and area are also equal, that is to say, they're congruent. Symbolically, given triangles ABC and DEF with AB = DE, AC = DF, and angle BAC = angle EDF, then the rest of the parts of the triangles are the same.
Guide to Book I, continued
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Book I Introduction
© 1999
D.E.Joyce
Clark University