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Pythagoras Basics 3

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

Level 1 Level 2 Level 3 Level 4 Exam-Style Three D Description Help More Pythagoras

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.

6.5cm

7cm

cm Correct Wrong

7.9cm

11.0cm

cm Correct Wrong

8.1cm

8.7cm

cm Correct Wrong

9.2cm

13.4cm

cm Correct Wrong

8cm

12.3cm

cm Correct Wrong

6.9cm

11.5cm

cm Correct Wrong

8.5cm

12.3cm

cm Correct Wrong

9.9cm

13.0cm

cm Correct Wrong

9.2cm

11.5cm

cm Correct Wrong

9.5cm

11.7cm

cm Correct Wrong

9.2cm

7.3cm

cm Correct Wrong

7.5cm

9.8cm

cm Correct Wrong
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This is Pythagoras Basics 3 level 3. You can also try:
Level 1 Level 2 Level 4

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.

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This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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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 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

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Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

QI,

Wednesday, June 12, 2019

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

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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Description of Levels

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Level 1 - Finding the hypotenuse

Level 2 - Finding a shorter side

Level 3 - Mixed questions

Level 4 - Pythagoras' Theorem 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.

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.

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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

So why is Pythagoras' theorem true?

The video above is from Australia's most unlikely new celebrity, Eddie Woo.

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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