A triangle ABC, ab = 5, BC = root 5, BC = double root 5. What shape is it

A triangle ABC, ab = 5, BC = root 5, BC = double root 5. What shape is it

∵AB=5,BC=√5,AC=2√5
∴BC²+AC²=（√5）²+（2√5）²=5+20=25=5²=AB²
ABC is RT (the inverse of Pythagorean theorem)

In triangle ABC, ab = radical 5-1, BC = radical 5 + 1, AC = 2 radical 3. Judge the shape of triangle ABC; find the height of AC side
Big brother, big sister,

Right triangles. Pythagorean theorem. Two thirds root sign 3

Given that a, B and C are three sides of △ ABC, and A2 + B2 + C2 = AB + AC + BC, then △ ABC is ()
A. Isosceles triangle B. right triangle C. equilateral triangle D. isosceles right triangle

The original formula can be reduced to 2A2 + 2B2 + 2c2 = 2Ab + 2Ac + 2BC, that is, A2 + B2 + C2 + A2 + B2 + c2-2ab-2ac-2bc = 0; according to the complete square formula, we can get: (a-b) 2 + (C-A) 2 + (B-C) 2 = 0; from the properties of non negative numbers, we can know that A-B = 0, C-A = 0, B-C = 0; that is, a = b = C. so △ ABC is an equilateral triangle, so we choose C