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Pythagoras' Theorem

A self marking exercise on the application of Pythagoras' Theorem.

Menu Level 0 Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Exam 3D Help More

Calculate the length of the third side of these right angled triangles. The diagrams are not to scale. Give your answer correct to 1 decimal place.

7.5cm

7.3cm

cm Correct Wrong

9.5cm

7.6cm

cm Correct Wrong

9.5cm

7.1cm

cm Correct Wrong

8.7cm

7.2cm

cm Correct Wrong

8.4cm

6.6cm

cm Correct Wrong

7.5cm

7.7cm

cm Correct Wrong
Check

This is Pythagoras' Theorem level 1. You can also try:
Level 2 Level 3 Level 4 Level 5 Level 6 Level 7

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

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Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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QI,

Wednesday, June 12, 2019

"The Babylonians were using Pythagoras' Theorem over 1,000 years before Pythagoras was born."

Ann Roberts, London

Thursday, October 1, 2020

"Three D Pythagoras
Suppose you have a cuboid with length l, width w and height h.
Can you find the longest internal length d from one corner to the opposite corner of the box, in terms of l, w and h ?
Your answer is the 3D-pythagoras formula.
NOTE: Being able to apply the 2D Pythagoras formula to 3D shapes is still an essential skill, especially if you have a more complex 3D shape."

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Description of Levels

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Level 0 - A 'whole number only' introductory set of questions

Level 1 - Finding the hypotenuse

Level 2 - Finding a shorter side

Level 3 - Mixed questions

Level 4 - Pythagoras coordinates

Level 5 - Mixed exercise

Level 6 - More than one triangle

Level 7 - Harder exercise

Exam Style questions requiring an application of Pythagoras' Theorem and trigonometric ratios to find angles and lengths in right-angled triangles.

Three Dimensions - Three dimensional Pythagoras and trigonometry questions

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Pythagoras' Theorem

The area of the square on the hypotenuse of a right angled triangle is equal to the sum of the areas of the squares on the two shorter sides.

Pythagoras' Theorem

You may have learned the theorem using letters to stand for the lengths of the sides. The corners (vertices) of the right-angled triangle is labelled with capital (upper case) letters. The lengths of the sides opposite them are labelled with the corresponding small (lower case) letters.

Pythagoras' Theorem

Alternatively the sides of the right-angled triangle may me named using the capital letters of the two points they span.

Pythagoras' Theorem

As triangle can be labelled in many different ways it is probably best to remember the theorem by momorising the first diagram above.

To find the longest side (hypotenuse) of a right-angled triangle you square the two shorter sides, add together the results and then find the square root of this total.

To find a shorter side of a right-angled triangle you subtract the square of the other shorter side from the square of the hypotenuse and then find the square root of the answer.

Example

Pythagoras Example

AB2 = AC2 - BC2
AB2 = 4.72 - 4.12
AB2 = 22.09 - 16.81
AB2 = 5.28
AB = √5.28
AB = 2.3m (to one decimal place)

 

The diagrams aren't always the same way round. They could be rotated by any angle.

Rotations

The right-angled triangles could be long and thin or short and not so thin.

Different proportions
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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