Criteria and properties of isosceles triangles.

A triangle is isosceles if and only if it has at least two equal sides. The angles opposite these equal sides are also equal. This property can be used to identify isosceles triangles and solve for unknown sides or angles.

Important properties

• If two sides of a triangle are equal, then the angles opposite those sides are equal.

• If two angles of a triangle are equal, then the sides opposite those angles are equal (converse).

• The altitude from the vertex angle (where the equal sides meet) to the base bisects the base and the vertex angle.

• The median and angle bisector from the vertex angle to the base coincide with the altitude.