Prove that an isosceles triangle with a 60° angle is equilateral (main problem 2).

An isosceles triangle has two sides with equal length and a base.

As a consequence, the two base angles are the same.

Now, there are two cases:

CASE 1: The 60° angle is the angle between the sides with equal length

In this case, we know that the two base angles must be the same, and together they form 180°-60°=120°. So, each of the base angle is a 60° angle, and so all three angles are 60° angles, and the triangle is equilateral

CASE 2: The 60° angle is one of the base angles

The other base angle must be a 60° angle as well. So, the two base angles form 120°, leaving 60° for the angle between the sides with equal length.

So, again, all three angles are 60°, and the triangle is equilateral.

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step-by-step explanation: