What Makes Each Quadrilateral Different

Four-sided shapes are usually taught as a list of names to memorise. This track treats them as one family instead, where each shape is the previous one with a single extra condition. It starts with the parallelogram, which assumes only that opposite sides are parallel and gets equal sides, equal opposite angles and bisecting diagonals for nothing — all of it falling out of the parallel-line angle work from earlier in the chapter. Adding equal sides gives a rhombus, whose diagonals cross at right angles and cut its corners in half; adding right angles instead gives a rectangle, whose diagonals become equal and turn the shape into four isosceles triangles. The trapezium and the kite then show what happens when a condition is dropped rather than added. The last tutorial ties it together by asking the only question that separates all four cleanly: what do the diagonals do?