Pythagorean ProbeUse Pythagoras' Theorem to help find all of the measurements of these right angles triangles. 
This is level 4: given two measurements. The diagrams are not drawn to scale. Include the letters 'cm' when labelling sides but the units of perimeters and areas are already typed for you.
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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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 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! Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry: "Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils. 
Whose Idea Was This?Did you enjoy doing this 'Pythagorean Probe' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept. 

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❎Pythagoras' Theorem Exercise  This would be a good place to start if you are a Pythagoras beginner.
Level 1  Given the lengths of two sides  Suitable for 
Level 2  Given two sides in different units  
Level 3  Given one short side and the area  
Level 4  Given two measurements  Suitable for 
Level 5  Given algebraic expressions for sides  
Level 6  Given expressions for the perimeter and area 
Exam Style Questions  A collection of problems in the style of GCSE or IB/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More on this topic including lesson Starters, visual aids, investigations and selfmarking exercises.
This exercise was inspired by a recource shared on Twitter by Nathan Day @nathanday314
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
See the National Curriculum page for links to related online activities and resources.
Did you do the main Pythagoras' Theorem Exercise yet? This is the video that mas made to help you with that exercise.
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. You can doubleclick the 'Check' button to make it float at the bottom of your screen. A tick or a cross will only appear if something has been typed into all of the input boxes for that question.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
This exercise was inspired by a recource shared on Twitter by Nathan Day @nathanday314
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