Geometry

Geometry taught as vocabulary is a list of names for shapes; taught as reasoning it is a small number of rules that force everything else. This track does the second. It opens by sorting triangles on one question — how many sides are equal — and shows that the angles then follow with nothing measured, because equal sides force equal angles. The second part proves the fact the first one leaned on twice: draw a single extra line and a triangle's three angles line up along it, which is why they total 180 degrees, and which is also why the rule fails on a globe. The third part takes the word 'same' apart, because same shape and same size are two different claims, and the difference is what makes maps, scale models and the whole of trigonometry work. Nothing here needs memorising once the reasoning is in place.