I would suggest 2 plane geometry theorems which may present some challenges.
The so-called "Side-splitter Theorem" which says that a line parallel to one side of a triangle splits the other two sides proportionally.
Ptolemy's Theorem which says that when a quadrilateral is inscribed in a circle, the product of the diagonals equals the sum of the products of the opposite sides. Of course, some of the corollaries of this theorem are instructive as well. For example, prove that the ratio of the perimeter of a regular pentagon to the side is the "golden ratio".
Another possible choice would be to prove that a line tangent to a circle from an external point is perpendicular to the radius at the point of tangency..
Also some of the theorems about bisectors, medians and altitudes of a triangle might also be included. There a probably lots of other contenders.
