# Pythagoras Theorem Questions

How to use the converse of Pythagorean Theorem to determine if a triangle is right angled
How to use the converse of Pythagorean Theorem to determine if a triangle is right angled

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.

 Pythagoras’ theorem $a^2 + b^2 = c^2$ where a,b and c are the sides of a right triangle.

Pythagoras’ theorem states that in a right triangle (or right-angled 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 formulas that can be deduced from the Pythagorean theorem

As a result of the formula $a^2 + b^2 = c^2$ we can also deduce that:

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 $?^2 = 16 + 36 = 52$

This gives us $? = \sqrt {52} = 7.21 \; cm \; to \; 2 \; decimal \; places$

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 $?^2 = 8^2 – 5^2 = 64 – 25 = 39$

This gives us $? = \sqrt {39} = 6.25 \; cm \; to \; 2 \; decimal \; places$

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 c2 = a2 + b2 then the triangle is a right triangle.

If Pythagoras’ theorem is false for the triangle, and c2 = a2 + b2 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 ‘real-life’ 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.

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.

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.

Using the sheets in this section will help you understand and answer a range of geometry questions.

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The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.