---
title: "Properties of triangles, quadrilaterals and circles"
description: "Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths"
canonical: https://lightmysky.com/learn/mathematics/properties-of-triangles-quadrilaterals-and-circles-mt_DNYQLahbfa
source: https://lightmysky.com/learn/mathematics/properties-of-triangles-quadrilaterals-and-circles-mt_DNYQLahbfa.md
retrieved: 2026-09-12
---

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# Properties of triangles, quadrilaterals and circles

Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

Subject: Mathematics · Area: Geometry · Ages 11 to 13
Page: https://lightmysky.com/learn/mathematics/properties-of-triangles-quadrilaterals-and-circles-mt_DNYQLahbfa

## Ready when they can

- List and verify properties of a parallelogram (opposite sides parallel/equal, opposite angles equal, diagonals bisect each other)
- Explain why a square is a special case of both a rectangle and a rhombus
- Derive the relationship between the radius, diameter, and circumference of a circle

## Lesson: Properties of Parallelograms, Squares, and Circles

A parallelogram is a four-sided shape where both pairs of opposite sides are parallel. In a parallelogram, opposite sides are always equal in length, and opposite angles are always equal to each other. The two diagonals also do something special: they bisect each other, meaning each diagonal cuts the other exactly in half at the point where they cross.

**Example.** Picture a parallelogram ABCD, where AB is opposite CD, and BC is opposite AD. If AB measures 6 cm, then CD also measures 6 cm, since opposite sides are equal. If angle A measures 70 degrees, then angle C, its opposite angle, also measures 70 degrees. Now draw both diagonals, AC and BD: they cross at one point, and that point splits each diagonal into two equal halves.

A rectangle is a parallelogram with four right angles. A rhombus is a parallelogram with four equal sides. A square fits both descriptions at once: it has four right angles, like a rectangle, and four equal sides, like a rhombus. That is why a square counts as a special case of both a rectangle and a rhombus, rather than being a separate shape on its own.

*(drawing: This square has four right angles, so it qualifies as a rectangle. It also has four equal sides, so it qualifies as a rhombus too.)*

**Tip.** For any circle, the diameter is always twice the radius: d = 2r. The circumference, the distance around the circle, is always about 3.14 times the diameter, written as C = pi times d. That number, pi, is the same for every circle, no matter how big or small.

**Recap.** Parallelograms have equal opposite sides and angles with diagonals that bisect each other, a square is a rectangle and a rhombus at once, and a circle's circumference is always pi times its diameter.

## Practice

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

## Needs first

- [Geometric terms and notation](https://lightmysky.com/learn/mathematics/geometric-terms-and-notation-mt_WtIFJSCQIT)
- [Parts of a circle](https://lightmysky.com/learn/mathematics/parts-of-a-circle-mt_xq3YHZ2zeR)

## Opens up

- [Congruent Triangles and the Congruence Conditions](https://lightmysky.com/learn/mathematics/congruent-triangles-and-the-congruence-conditions-mt_it8t7mY71J)