---
title: "Classifying shapes by properties"
description: "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 hi"
canonical: https://lightmysky.com/learn/mathematics/classifying-shapes-by-properties-mt_liIW336odh
source: https://lightmysky.com/learn/mathematics/classifying-shapes-by-properties-mt_liIW336odh.md
retrieved: 2026-10-19
---

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# 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

Subject: Mathematics · Area: Geometry · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/classifying-shapes-by-properties-mt_liIW336odh

## Ready when they can

- 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

## Lesson: Shape families: rectangles, squares, and more

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.

*(drawing: A square has every property a rectangle needs, plus one more: all 4 sides equal.)*

**Example.** 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.

**Tip.** 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.

**Recap.** A shape belongs to every family whose rules it meets, from the biggest group down to the most exact match.

## Practice

18 questions on this page, each with its working shown.

## Needs first

- [Regular and irregular polygons](https://lightmysky.com/learn/mathematics/regular-and-irregular-polygons-mt_8H2kO4k2B9)
- [Classifying shapes by line properties](https://lightmysky.com/learn/mathematics/classifying-shapes-by-line-properties-mt_r8c43QB6wx)

## Opens up

- [Scale and similar shapes](https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW)
- [Angles in triangles (age 10+)](https://lightmysky.com/learn/mathematics/angles-in-triangles-age-10-mt_cdMlC7EpTJ)
- [Using structure in shapes and expressions](https://lightmysky.com/learn/mathematics/using-structure-in-shapes-and-expressions-mt_hImiKNiaNh)
- [Area of Triangles & Parallelograms](https://lightmysky.com/learn/mathematics/area-of-triangles-and-parallelograms-mt_ML5t7n2-U8)
- [Geometric terms and notation](https://lightmysky.com/learn/mathematics/geometric-terms-and-notation-mt_WtIFJSCQIT)