--- 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: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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 have sorted shapes by their sides and angles. A quadrilateral is a polygon with four straight sides. A shape belongs to every family whose rules it meets. A more specific family name does not remove a broader one. *(drawing: A square has four equal sides and four right angles. Check both properties when sorting it.)* **Example.** Mia's sandpit has four sides of 4 m and four right angles. A rectangle has four right angles and equal opposite sides. A square has four right angles and four equal sides. The sandpit meets both rules, so it is a square and a rectangle. Every square is a rectangle. The reverse is not always true: a rectangle can have unequal neighbouring sides. Here, quadrilaterals have sides that do not cross. A parallelogram is a quadrilateral with two pairs of parallel opposite sides. Its opposite sides are equal in length. Going round it, the lengths repeat: one length, another length, then those two again. Neighbouring sides need not match. The reverse also holds: if both pairs of opposite sides are equal in length, the quadrilateral is a parallelogram. Rectangles are parallelograms with four right angles. Rhombuses are parallelograms with four equal sides. Squares have both extras. A parallelogram with no right angles and unequal neighbouring sides fits neither smaller family. Knowing only that opposite sides are parallel does not tell you which extras the shape has. A hierarchy diagram shows families inside broader families. Put parallelograms inside quadrilaterals. Inside parallelograms, rectangle and rhombus regions overlap. Put squares in their overlap because squares meet both rules. The path below follows just the rectangle branch. Each later family is inside the one before it. **Example.** To sort a collection, check each shape separately and keep every matching name. Then count only what the question asks for. Mia's square sandpit has five of our family names: quadrilateral, parallelogram, rectangle, rhombus and square. If asked for its most specific name, choose square. That name includes both the equal-side and right-angle rules. Regular polygons have all sides equal and all angles equal. Squares are regular. Non-square rectangles have unequal neighbouring sides; non-square rhombuses have unequal angles. So a parallelogram need not be regular. To challenge an 'every' claim, find a counterexample: a shape in the named family that lacks the claimed property. Turning a shape leaves its side lengths and angles unchanged. A uniform enlargement makes the whole shape bigger by the same scale factor, keeping every angle unchanged. With scale factor 2, every side doubles. Equal sides stay equal and unequal sides stay unequal; parallel pairs stay parallel. Turning and uniform enlargement preserve shape families and regularity. **Recap.** A shape belongs to every family whose rules it meets, from the biggest group down to the most exact match. *This lesson and its practice material were written for this dataset.* ## 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)