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Isosceles Triangles

An isosceles triangle is a triangle with at least two equal sides, meaning that the lengths of those sides are equal. A new set of terms accompanies the isosceles triangle. The equal sides are called legs. The third side is the base. The angle opposite the base is the vertex angle. The angles opposite the legs are called the base angles.

Figure %: A generic isosceles triangle
Sides a and b are the legs. Side c is the base. Angle C is the vertex angle. Angles A and B are the base angles.

The beauty of an isosceles triangle is that, just like the sides, the base angles are equal. From this we learn that if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is an isosceles triangle. We also know the converse: if two sides of a triangle are equal, their opposite angles are equal, and the triangle is isosceles.