Can you use Proof by Induction to establish what will happen when you add more and more odd numbers?
Can you prove that a quadrilateral drawn inside a tetrahedron is a parallelogram?
Do you have enough information to work out the area of the shaded quadrilateral?
Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.
Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
