Mathematics

Mathematics

Problem

Consider two triangles △ABC\triangle ABC and △DEF\triangle DEF. a. (i) Define the term "included angle" of a pair of sides of a triangle. b. (ii) It is given that AB=DEAB = DE, AC=DFAC = DF and ∠BAC=∠EDF\angle BAC = \angle EDF. Are the two triangles necessarily congruent? If yes, name the congruence criterion applied and give a brief reason. c. (iii) Suppose instead of the equality in part (ii) it is known that ∠ABC=∠DEF\angle ABC = \angle DEF while the side equalities remain the same. Does this new set of data guarantee congruence? Give a short justification for your answer.

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