Classifying shapes by properties
Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties
What a learner can do afterwards
- Explain why all squares are rectangles but not all rectangles are squares
- Place quadrilaterals in a hierarchy diagram showing subset relationships
- Identify properties shared by all parallelograms and explain why rhombuses and rectangles are special cases
The lesson
You already know how to describe shapes by their sides and angles. Now use those same properties to sort shapes into families. A shape can belong to more than one family at once: a big general family, and a smaller, more exact family inside it.
A rectangle needs 4 right angles and opposite sides equal. A square has 4 right angles and all 4 sides equal, so it passes every rectangle test too. That is why every square is a rectangle. But not every rectangle is a square, since a rectangle's sides do not all have to match.
The parallelogram family is even bigger. Every parallelogram has two pairs of parallel, equal-length sides. A rectangle is a parallelogram that also has 4 right angles. A rhombus is a parallelogram that also has 4 equal sides. A square has both extras, so it is a rectangle and a rhombus at the same time.
To sort a shape, check which rules it passes. If it passes a family's rules, it belongs there, even when it also fits inside a smaller, more exact family.
A shape belongs to every family whose rules it meets, from the biggest group down to the most exact match.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.