Quadrilaterals
Four straight sides can close up in endless ways. Which four-sided shapes earn a name, and what does each name promise?
Where you are 7 inside
What this area is about
A quadrilateral is a flat polygon with four sides. A few conditions on sides, angles or parallel pairs pick out shapes with names, and each name carries facts nobody had to measure. The names are inclusive, so one shape can carry several.
How these fit together
First names. Rhombuses, rectangles and squares are sorted with a ruler and the corner of a card, and shapes in more than one category shows that a square is all three, while many quadrilaterals are none.
Definitions and the family tree. What each special quadrilateral guarantees lists the promises behind each name, and the quadrilateral family tree places square, rectangle, rhombus, parallelogram, trapezoid and kite inside one another.
Results. Properties of a parallelogram: if both pairs of opposite sides are parallel, then opposite sides and opposite angles are congruent, neighboring angles add to 180^\circ, and the diagonals bisect each other. Rectangles, rhombuses and squares add more: a rectangle’s diagonals are congruent, a rhombus’s are perpendicular. In trapezoids and kites, the two angles along each leg of a trapezoid add to 180^\circ, an isosceles trapezoid has equal base angles and congruent diagonals, and a kite’s diagonals are perpendicular.
A path through it
Rhombuses, rectangles and squares, then shapes in more than one category, then what each quadrilateral guarantees. Parallelograms come next, then rectangles and rhombuses, then trapezoids and kites, and the family tree last, since it gathers them all.
After this come proofs about parallelograms, angle sums of polygons and midsegments of trapezoids.