L3 · The Quadrilateral Hierarchy

Learning goal

“I can sort quadrilaterals into their families using their properties, and I can explain why a special shape like a square belongs to several families at once.”

Quadrilateral — any polygon with exactly four sides. Every shape in this lesson is one.

Hierarchy — a family tree for shapes: a shape in a lower, more special family keeps ALL the properties of every family above it.

Parallelogram — a quadrilateral with two pairs of parallel sides. (Its opposite sides are equal in length.)

Rhombus — a parallelogram with all four sides equal in length.

Worked example

Learn each family's property list - these lists are the ONLY judges in this lesson. Parallelogram: two pairs of parallel sides; opposite sides equal in length. Rectangle: a parallelogram PLUS four right angles. Rhombus: a parallelogram PLUS all four sides equal in length. Square: a parallelogram PLUS all sides equal AND four right angles - it has every property on the list. Trapezoid: a quadrilateral with a pair of parallel sides (it does not promise two pairs). Now classify: a quadrilateral with two pairs of parallel sides, sides 6, 4, 6, 4, and NO right angles. Two pairs parallel -> parallelogram family. No right angles -> not a rectangle, not a square. Sides not all equal -> not a rhombus. Verdict: parallelogram - that is its most special name.

Check yourself — explain it

What decides a quadrilateral's family?

Paired problem — example still visible

Classify: all four sides 7 cm, four right angles, two pairs of parallel sides -> Square (every property present)

Faded completion — last step is yours

"A parallelogram with all four sides equal is called a ___" -> rhombus

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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