If one of the angles of an isosceles triangle is 60 degrees, is it an equilateral triangle?

Let in the triangle ABC AB = BC, and the angle BAC = 60.

Let’s build the height BH to the base of the AC, which is also the bisector and median of the triangle.

Then the angle ABH = CBH = ABC / 2 = 60/2 = 30, AH = CH, and the triangles ABH and CBH are rectangular.

In a right-angled triangle ABH, leg AH lies opposite angle 30, then AH = AB / 2.

Since AH = CH, then AC = 2 * AH = 2 * AB / 2 = AB.

AB = AC = BC, then the triangle ABC is equilateral.

Answer: The ABC triangle is equilateral.