Pythagoras' Theorem ExerciseA self marking exercise on the application of Pythagoras' Theorem. 
Here are some questions which can be answered using Pythagoras' Theorem. You can earn a trophy if you get at least 9 questions correct. Each time you finish a question click the 'Check' button lower down the page to see if you got it right!
The last four questions were shared by Dr Colin Foster, Reader in Mathematics Education in the Mathematics Education Centre at Loughborough University, at his keynote address to the Mathematical Association as his some of his favourite "Pythagoras" tasks.
This is Pythagoras' Theorem Exercise level 6. You can also try:
Level 1
Level 2
Level 3
Level 4
Level 5
InstructionsTry 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. 



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Level 1  Finding the hypotenuse
Level 2  Finding a shorter side
Level 3  Mixed questions
Level 4  Pythagoras coordinates
Level 5  Pythagoras' Theorem exercise
Level 6  Pythagoras' Theorem harder exercise
Exam Style questions requiring an application of Pythagoras' Theorem and trigonometric ratios to find angles and lengths in rightangled triangles.
Three Dimensions  Three dimensional Pythagoras and trigonometry questions
More on this topic including lesson Starters, visual aids, investigations and selfmarking exercises.
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See the National Curriculum page for links to related online activities and resources.
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.
You may have learned the theorem using letters to stand for the lengths of the sides. The corners (vertices) of the rightangled triangle is labelled with capital (upper case) letters. The lengths of the sides opposite them are labelled with the corresponding small (lower case) letters.
Alternatively the sides of the rightangled triangle may me named using the capital letters of the two points they span.
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 rightangled 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 rightangled 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.
AB^{2} = AC^{2}  BC^{2}
AB^{2} = 4.7^{2}  4.1^{2}
AB^{2} = 22.09  16.81
AB^{2} = 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.
The rightangled triangles could be long and thin or short and not so thin.
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