An isosceles triangle has two sides of equal length. The angles
opposite the equal sides are also equal. These two angles are called the base angles.

Example:
An isosceles triangle has one angle of
96º. What are the sizes of the other two angles?

Solution: Step 1: Since it is an isosceles
triangle it will have two equal angles. The given 96º angle cannot
be one of the equal pair because a triangle cannot have two obtuse
angles..

Step 2: Let x be one of
the two equal angles. The sum of all the angles in any triangle
is 180°. x + x + 96° = 180°
Þ
2x = 84°
Þx = 42°

Answer: The sizes of the other
two angles are 42º each.

An equilateral triangle has all three sides equal in length. Its
three angles are also equal and they are each 60º. Therefore, an equilateral triangle is also an equiangular triangle.

An equilateral triangle can be considered a special case of isosceles triangle, having all three sides equal.