is greater than either of the two sides and less than their sum.

The second part of this theorem is already established above for any side of any triangle. The first part is established using the lower figure. In the figure, consider the right triangle . An isosceles triangle is constructed with equal sides . From the triangle postulate, the angles in the right triangle satisfy:
:Likewise, in the isosceles triangle , the angles satisfy:
:Therefore,
:and so, in particular,
:That