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Pythagoras Theorem

Pythagoras Theorem. Calculating the Hypotenuse. Solving real-life problems. Finding the length of the smaller side. Mixed Problems. www.mathsrevision.com. Distance between two points. Exam Type Questions. Starter Questions. www.mathsrevision.com. Calculating Hypotenuse.

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Pythagoras Theorem

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  1. Pythagoras Theorem Calculating the Hypotenuse Solving real-life problems Finding the length of the smaller side Mixed Problems www.mathsrevision.com Distance between two points Exam Type Questions Compiled by Mr. Lafferty Maths Dept.

  2. Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  3. Calculating Hypotenuse Learning Intention Success Criteria • Remember the term hypotenuse “ the longest side” • We are learning to use Pythagoras Theorem to calculate the length of the hypotenuse • “the longest side” • Apply Pythagoras Theorem to calculate the hypotenuse. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  4. Calculating the Hypotenuse Level 4 Example 1 Calculate the longest length of the right- angled triangle below. c 8 www.mathsrevision.com 12 Compiled by Mr. Lafferty Maths Dept.

  5. Calculating the Hypotenuse Level 4 Example 2 An aeroplane is preparing to land at Glasgow Airport. It is over Lennoxtown at present which is 15km from the airport. It is at a height of 8km. How far away is the plane from the airport? Aeroplane www.mathsrevision.com c b = 8 a =15 Airport Lennoxtown Compiled by Mr. Lafferty Maths Dept.

  6. Calculating Hypotenuse Now try TJ4+ Ex 13.1 Ch13 (page 92) www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  7. Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  8. Solving Real-Life Problems Learning Intention Success Criteria • Be able to solve real-life problems using Pythagoras Theorem showing clear working. 1. We are learning how Pythagoras Theorem can be used to solve real-life problems. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  9. Solving Real-Life Problems 15m rod 8m When coming across a problem involving finding a missing side in a right-angled triangle, you should consider using Pythagoras’ Theorem to calculate its length. Example : A steel rod is used to support a tree which is in danger of falling down. What is the length of the rod? www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  10. Solving Real-Life Problems Example 2 A garden is rectangular in shape. A fence is to be put along the diagonal as shown below. What is the length of the fence. www.mathsrevision.com 10m 15m Compiled by Mr. Lafferty Maths Dept.

  11. Solving Real-Life Problems Now try TJ4+ Ex 13.2 Ch13 (page 94) www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  12. Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  13. Length of the smaller side Learning Intention Success Criteria • Apply Pythagoras Theorem to find the length of smaller side showing clear working. 1. We are learning how Pythagoras Theorem can be used to find the length of the smaller side. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  14. Length of the smaller side 20cm 12cm a cm To find the length of the smaller side of a right- angled triangle we simply rearrange Pythagoras Theorem. Example : Find the length of side a ? Check answer ! Always smaller than hypotenuse www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  15. Length of the smaller side 10cm b cm 8 cm Example : Find the length of side b ? Check answer ! Always smaller than hypotenuse www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  16. Length of smaller side Now try TJ4+ Ex 13.3 Ch13 (page 96) www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  17. Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  18. Pythagoras Theorem Finding hypotenuse c Finding shorter side b c b a www.mathsrevision.com Finding shorter side a Compiled by Mr. Lafferty Maths Dept.

  19. A rectangular metal grill for a window is shown below. Two diagonal metal bars strengthen the grill. Find the length of one of the metal bars.

  20. A steel plate in the shape of an isosceles triangle is used to strengthen a bridge. Calculate the height of the steel plate. Do not use a scale drawing. 1.2 m height 3.6 m

  21. Pythagoras Theorem Now try TJ4+ Ex 13.4 Ch13 (page 97) www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  22. Starter Questions www.mathsrevision.com

  23. Finding the Length of a Line Learning Intention Success Criteria • Apply Pythagoras Theorem to find length of a line. 1. We are learning how Pythagoras Theorem can be used to find the length of a line. • 2. Show all working. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  24. Discuss with your partner how we might find the length of the line. Finding the Length of a Line Level 4 8 (7,7) 7 6 3 5 5 4 (2,4) www.mathsrevision.com 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Created by Mr. Lafferty Maths Dept.

  25. Pythagoras Theorem to find the length of a Line Level 4 8 7 (0,6) 6 5 4 5 www.mathsrevision.com 3 2 (9,1) 9 1 0 1 2 3 4 5 6 7 8 9 10 Created by Mr. Lafferty Maths Dept.

  26. Have you updated your Learning Log ? Pythagoras Theorem Now try TJ4+ Ex 13.5 Ch13 (page 99) www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  27. 4 marks

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