Quadrilateral family tree

Six four-sided shapes arranged as a family rather than a vocabulary list. Follow a branch downward and every property above it still belongs to the shape below.

Quadrilateral family — free printable reference chart

Reference chart

Quadrilateral family tree

Quadrilateral4 straight sides
Trapezoidexactly 1 pair parallel
Parallelogram2 pairs parallel
Rectangle4 right angles
Rhombus4 equal sides
Square4 equal sides + 4 right angles

A square belongs to both branches: it is a rectangle and a rhombus. This chart uses “trapezoid” for exactly one pair of parallel sides.

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What's on this chart

A square is not beside a rectangle in this chart as though the two were different species. It sits below both rectangle and rhombus, because it has four right angles and four equal sides at the same time. That is the classification idea children miss when each shape arrives on its own flashcard: a figure can have more than one true name, and the more specific name does not erase the larger family it came from.

Why this chart helps

The pictures and properties stay together. Parallel sides are not a word to memorize after looking away from the figure; they are the reason the parallelogram branch exists. Four right angles take that branch to rectangle, four equal sides take it to rhombus, and satisfying both descriptions brings the two paths back together at square.