Home -> Reference -> Geometry - Checking Right Angles# Geometry - Checking Right Angles

## Using a Sheet of Paper

## Using a Pythagorean Triangle

An article by Andy Slater with illustrations by Aris Kafantaris.

The concept of a right angle (a 90° angle) is a fundamental concept which is understood by most people, even if they can't define it. In this article we're going to assume that you know what they are, forget all about fancy mathematical definitions, and deal with the problem of how to check whether something is a right angle or not. What's more, we are going to do it without the aid of a protractor, or even a safety net!

The first technique is to use a sheet of paper. Don't be tempted to assume that the corner of the paper is a right angle because it might not be. Instead, fold the paper in half. The fold should be perfectly straight i.e. 180°. Now fold the paper in half again such that the folded edge is divided into two and the corner that you've made should be a perfect 90° right angle.

Our second technique is to use the 345 triangle of Pythagorean fame. This technique is particularly worth knowing for when you need to check really big right angles. What you do is to measure 3 units along one side of the angle that you want to check and 4 units along the other. The diagonal distance between them will be 5 units if, and only if, the corner is a right angle. Note that the 'units' can be anything you like: centimetres, feet, lengths of your garden spade, i.e. whatever you have to hand.

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