In △ ABC, if C = 60 ° and C2 = AB, then the shape of triangle is () A. Right triangle B. isosceles triangle C. equilateral triangle D. obtuse triangle

In △ ABC, if C = 60 ° and C2 = AB, then the shape of triangle is () A. Right triangle B. isosceles triangle C. equilateral triangle D. obtuse triangle

∵ C = 60 °, ∵ C2 = A2 + b2-2abcos60 ° = A2 + b2-ab ∵ C2 = AB, ∵ A2 + b2-ab = AB, that is, A2 + b2-2ab = 0, then (a-b) 2 = 0 ∵ a = B, combined with C = 60 ° to get △ ABC is an equilateral triangle, so select: C