You are an isosceles triangle that has two equal sides and two equal angles.
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An Isosceles Triangle
That is what is called an equilateral triangle.
An isosceles triangle has two sides that are equal in length and thus two equal angles.
All angles equal = all sides equal = equilateral. Two angles equal = two sides equal = isosceles. All angles different = all sides different = scalene. An isosceles or scalene triangle may be right-angled or obtuse-angled if one of its angles is a right angle or obtuse angle (respectively).
If an isosceles triangle is defined as one which has two sides (or angles) equal, then YES. But if an isosceles triangle is defined as one which has two sides (or angles) equal, and the third side (angle) different, then NO.