Michael C. answered • 03/17/17

Tutor

4.9
(10)
Patient and Qualified Math Tutor

Triangles ABC and DEF

angle B = angle E

side AB = side DE and

side BC = side EF

It is accepted by standard procedure that given the above the triangles ABC and DEF are congruent by SAS

However if further proof is needed consider the cosine formula; AC

^{2}= AB^{2}+ BC^{2}-2*AB*BC * cosB ; applied to the triangle DEF; DF^{2}= DE^{2}+ EF^{2}- 2*DE*EF*cosE, since AB=DE, and BC = EF and angles E and B are equal, then it stands to reason that AC = DF and would give the third side as being equal as well. Hence both triangles are congruent.