---
title: "Classifying shapes by line properties"
description: "Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category"
canonical: https://lightmysky.com/learn/mathematics/classifying-shapes-by-line-properties-mt_r8c43QB6wx
source: https://lightmysky.com/learn/mathematics/classifying-shapes-by-line-properties-mt_r8c43QB6wx.md
retrieved: 2026-10-19
---

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# Classifying shapes by line properties

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category

Subject: Mathematics · Area: Geometry · Ages 9 to 10
Page: https://lightmysky.com/learn/mathematics/classifying-shapes-by-line-properties-mt_r8c43QB6wx

## Ready when they can

- Sort a set of quadrilaterals into those with parallel sides and those without
- Identify which triangles in a set are right triangles
- Classify shapes that have both perpendicular and parallel sides

## Lesson: Sorting Shapes by Their Lines

You have sorted quadrilaterals by their sides before: how many, how long, which ones match. The lines themselves give you a second way to sort. Two sides are parallel when they run the same way and never meet, however far you stretch them. On a plan, matching arrows mark a parallel pair. A rectangle has two pairs of parallel sides, and so does a square. A triangle has only three sides, so it can never make two pairs.

**Example.** Omar holds the corner of a book page against one corner of a triangle. It fits exactly, so that corner is a right angle, and the two sides meeting there are perpendicular. On a drawing, a small square inside the corner is the mark for a right angle. One right angle is enough to call the whole shape a right triangle. The other two corners can be any size.

Now sort with both clues at once. A square shows both: its opposite sides are parallel, and every corner is a right angle, so sides that meet there are perpendicular. A right triangle shows only one. Its two sides at the square corner are perpendicular, but none of its three sides run parallel to another. So a right angle does not promise parallel sides.

*(drawing: A rectangle carries both clues: two pairs of parallel sides, and a right angle in every corner.)*

**Tip.** Sorting fast: hunt for the arrows first, then the square corners. Two sides that lean towards each other are not parallel, even if they have not met yet on the page.

**Recap.** Sort shapes by their lines: arrows mark a parallel pair, a small square marks a right angle, and the two clues can turn up together, one at a time, or not at all.

## Practice

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

## Needs first

- [Sorting 2-D and 3-D shapes](https://lightmysky.com/learn/mathematics/sorting-2-d-and-3-d-shapes-mt_fEuoBYw6bU)
- [Lines, Rays & Angles](https://lightmysky.com/learn/mathematics/lines-rays-and-angles-mt_QysgF57dxh)
- [Classifying quadrilaterals](https://lightmysky.com/learn/mathematics/classifying-quadrilaterals-mt_Xt1cRqaBOW)

## Opens up

- [Classifying shapes by properties](https://lightmysky.com/learn/mathematics/classifying-shapes-by-properties-mt_liIW336odh)
- [Parts of a circle](https://lightmysky.com/learn/mathematics/parts-of-a-circle-mt_xq3YHZ2zeR)