Theorem 16 - Base times Height in a Triangle
A triangle has three choices for base and each one has a corresponding height (shown in the same colour with a dotted line). This demonstrates that when a base is multiplied by the corresponding height the answer is the same regardless of the choice of base.
Drag the points X, Y or Z to change the shape of the triangle. In particular, try to create an obtuse-angled triangle. Notice that the product of the base and the corresponding height is the same for each base. What is the point of intersection of the heights called? (See construction 22). When does this point appear outside the triangle.