SOLUTION: In triangle ABC, AB + 2(BC) = BC + 2(AB) and AC + 2(AB) = AB + 2(AC). Classify triangle ABC. A. Scalene B. Isosceles C. Equilateral D. Right

Algebra ->  Triangles -> SOLUTION: In triangle ABC, AB + 2(BC) = BC + 2(AB) and AC + 2(AB) = AB + 2(AC). Classify triangle ABC. A. Scalene B. Isosceles C. Equilateral D. Right       Log On


   

Question 509239: In triangle ABC, AB + 2(BC) = BC + 2(AB) and AC + 2(AB) = AB + 2(AC). Classify triangle ABC.
A. Scalene
B. Isosceles
C. Equilateral
D. Right

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We note that the two equations are equivalent to "AB = BC" and "AB = AC." Hence, AB = BC = AC and the triangle is equilateral. Equilateral triangles are sometimes defined to be isosceles as well.