An Isosceles triangle is a special triangle in which two of its sides are of equal length and the angles opposites the equal sides are also equal. These equal angles are called the base angles. Let's examine the isosceles below and then process to its script to explore further.

Remember that the base and altitude are given. With an isosceles triangle the altitude will also be the perpendicular-bisector. This is because the vertex D lies on the altitude and is equidistant from vertex A and B. This equidistance of DA and DB forms the two equal sides of the triangle.

Let's start with the given base AB and the altitude DC. Since it is an isosceles the altitude will also be the perpendicular-bisector. Knowing this we first find the midpoint of AB, then we construct the perpendicular to AB. The midpoint gives us the bisection, and the perpendicular gives us the perpendicular. So together we have a perpendicular-bisector.

To find the equal sides we construct two circles. One circle is formed using point B as the center. The other circle is formed using point A as the center. The point of intersection of the two circles gives us the formation of the two equal sides. AD = DB because they are the radii of equal-sized circles.