Explore some of the different types of network, and prove a result about network trees.
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Can you prove Pythagoras' Theorem using enlargements and scale factors?
You could start by considering a simpler case, such as the one below:
If angle $BAC = x$, what other angles can you find? Can you find angle $ABC$ in terms of $x$? Can you find angle $CBD$ in terms of $x$?...