Welcome to our Pythagoras' Theorem Questions area.
Here you will find help, support and questions to help you master Pythagoras' Theorem and apply it.
Here you will find our support page to help you learn to use and apply Pythagoras' theorem.
Please note: Pythagoras' Theorem is also called 'The Pythagorean Theorem'
There are a range of sheets involving finding missing sides of right triangles, testing right triangles and solving word problems using Pythagoras' theorem.
Using these sheets will help your child to:

Pythagoras' theorema^{2} + b^{2} = c^{2}where a,b and c are the sides of a right triangle. Side c is the hypotenuse (longest side). 
Pythagoras' theorem states that in a right triangle (or rightangled triangle) the sum of the squares of the two smaller sides of the triangle is equal to the square of the hypotenuse.
In other words, a^{2} + b^{2} = c^{2}.
where c is the hypotenuse (the longest side) and a and b are the other sides of the right triangle.
What does this mean?
This means that for any right triangle, the orange square (which is the square made using the longest side) has the same area as the other two blue squares added together.
Other formulae
As a result of the formula a^{2} + b^{2} = c^{2}, we can also deduce that:
Example 1
In this example, we need to find the hypotenuse (longest side of a right triangle).
So using pythagoras, the sum of the two smaller squares is equal to the square of the hypotenuse.
This gives us 4^{2} + 6^{2} = ?^{2}
So ?^{2} = 16 + 36 = 52
So ? must be equal to √52 = 7.21cm to 2dp.
Example 2
In this example, we need to find the length of the base of the triangle, given the other two sides.
So using pythagoras, the sum of the two smaller squares is equal to the square of the hypotenuse.
This gives us ?^{2} + 5^{2} = 8^{2}
So ?^{2} = 8^{2}  5^{2} = 64  25 = 39
So ? = √39 = 6.25cm to 2dp.
The following questions involve using Pythagoras' theorem to find the missing side of a right triangle.
The first sheet involves finding the hypotenuse only.
A range of different measurement units have been used in the triangles, which are not drawn to scale.
The following questions involve using Pythagoras' theorem to find out whether or not a triangle is a right triangle, (whether the triangle has a right angle).
If Pythagoras' theorem is true for the triangle, and c^{2} = a^{2} + b^{2} then the triangle is a right triangle.
If Pythagoras' theorem is false for the triangle, and c^{2} = a^{2} + b^{2} then the triangle is not a right triangle.
A range of different measurement units have been used in the triangles, which are not drawn to scale.
The following questions involve using Pythagoras' theorem to solve a range of word problems involving 'reallife' type questions.
On the first sheet, only the hypotenuse needs to be found, given the measurements of the other sides.
Illustrations have been provided to support students solving these word problems.
Here you will find a support page packed with a range of geometric formula.
Included in this page are formula for:
This page will provide a useful reference for anyone needing a geometric formula.
Here you will find a support page to help you understand some of the special features that triangles have, particularly right triangles.
Using this support page will help you to:
All the free printable geometry worksheets in this section support the Elementary Math Benchmarks.
Here you will find a range of geometry cheat sheets to help you answer a range of geometry questions.
The sheets contain information about angles, types and properties of 2d and 3d shapes, and also common formulas associated with 2d and 3d shapes.
Included in this page are:
Using the sheets in this section will help you understand and answer a range of geometry questions.
How to Print or Save these sheets
Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!
How to Print or Save these sheets
Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!
The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.
We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.
Do you know how old you are...in weeks? days? hours?
Are you more than a million minutes old?
Find out how old you are to the nearest second!
Looking for some fun printable math games?
We have some great games for you to play in our Math Games ebooks!
Have a look at some of our most popular pages to see different Math activities and ideas you could use with your child
If you are a regular user of our site and appreciate what we do, please consider making a small donation to help us with our costs.
Get a free sample copy of our Math Salamanders Dice Games book with each donation!
Looking for a fun and motivating way to learn and practice math skills?
Why not try one of our free printable math games with your students!
New! Comments
Have your say about the Math resources on this page! Leave me a comment in the box below.