Thales was also a big hit outside of Greece. In Egypt he made a name for himself by successfully measuring pyramids. Cleverly, he measured the pyramid's shadow at the time of the day when his shadow was equal to his height. His contributions to geometry are the following theorems:
A circle is bisected by its diameter.
The angles at the bases of any isosceles triangle are equal.
If two straight lines cut one another, the opposite angles are equal. (see below)
If two triangles have two angles and a side in common, the triangles are identical.