A triangle which has two of its sides equal in length.

Try this Drag the orange dots on each vertex to reshape the triangle.
Notice it always remains an isosceles triangle, the sides AB and AC always remain equal in length

The word isosceles is pronounced "eye-sos-ell-ease" with the emphasis on the 'sos'. It is any triangle that has two sides the same length.

If all three sides are the same length it is called an
equilateral triangle.
Obviously all equilateral triangles also have all the properties of an isosceles triangle.

Properties

The unequal side of an isosceles triangle is usually referred to as the 'base' of the triangle.

The base angles of an isosceles triangle are always equal.
In the figure above, the angles ∠ABC and ∠ACB are always the same

When the 3rd angle is a right angle, it is called a "right isosceles triangle".

The altitude is a perpendicular distance from the base to the topmost vertex.

Constructing an Isosceles Triangle

It is possible to construct an isosceles triangle of given dimensions using just a compass and straightedge. See these three constructions:

If you are given one
interior angle
of an isosceles triangle you can find the other two.

For example, We are given the angle at the apex as shown on the right of 40°.
We know that the interior angles of all triangles add to 180°.
So the two base angles must add up to 180-40, or 140°. Since the two base angles are congruent (same measure), they are each 70°.

If we are given a base angle of say 45°, we know the base angles are congruent (same measure)
and the interior angles of any triangle always add to 180°. So the apex angle must be 180-45-45 or 90°.