Question

A trigonometry student makes the statement, “if we know any two sides and one angle of a triangle, then the triangle is uniquely determined.” Is this a valid statement? Explain, referring to the congruence axioms.

Answer 1

In fact, each side of the triangle and, by consequence, its adjacent angles, are determined by the other two sides and its opposite angle. This imply that, if any two triangles have two equal sides forming a same angle, then the triangles are congruent.

Therefore, the statement is valid.