A point P is selected anywhere inside an equilateral triangle. What
can you say about the sum of the perpendicular distances from P to
the sides of the triangle? Can you prove your conjecture?
Can you make sense of the three methods to work out the area of the kite in the square?
We are given a regular icosahedron having three red vertices. Show
that it has a vertex that has at least two red neighbours.
Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.