1 / 40

Pythagoras Theorem

S3 Credit. Pythagoras Theorem. Investigating Pythagoras Theorem. Finding the length of the smaller side. Solving Real – Life Problems. www.mathsrevision.com. Pythagoras Theorem Twice. Converse of Pythagoras Theorem. Starter Questions. Q1. Explain why 4 + 6 x 5 = 34 and not 50 .

zachary
Download Presentation

Pythagoras Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. S3 Credit Pythagoras Theorem Investigating Pythagoras Theorem Finding the length of the smaller side Solving Real – Life Problems www.mathsrevision.com Pythagoras Theorem Twice Converse of Pythagoras Theorem Compiled by Mr. Lafferty Maths Dept.

  2. Starter Questions Q1. Explain why 4 + 6 x 5 = 34 and not 50 Q2. Calculate www.mathsrevision.com Q3. Does x2 – 121 factorise to (x – 11) (x - 11) Q4. The cost of an iPod is £80 including VAT. How much is the iPod BEFORE VAT. NON-CALCULATOR Compiled by Mr. Lafferty Maths Dept.

  3. Right – Angle Triangles Aim of today's Lesson ‘To investigate the right-angle triangle and to come up with a relationship between the lengths of its two shorter sides and the longest side which is called the hypotenuse. ‘ www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  4. Right – Angle Triangles 3 What is the length of a? 4 What is the length of b ? www.mathsrevision.com Copy the triangle into your jotter and measure the length of c 5 Compiled by Mr. Lafferty Maths Dept.

  5. Right – Angle Triangles What is the length of a? 6 8 What is the length of b ? www.mathsrevision.com Copy the triangle into your jotter and measure the length of c 10 Compiled by Mr. Lafferty Maths Dept.

  6. Right – Angle Triangles 5 What is the length of a? 12 What is the length of b ? www.mathsrevision.com Copy the triangle into your jotter and measure the length of c 13 Compiled by Mr. Lafferty Maths Dept.

  7. Right – Angle Triangles Copy the table below and fill in the values that are missing www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  8. Right – Angle Triangles Can anyone spot a relationship between a2, b2, c2. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  9. Pythagoras’s Theorem c b www.mathsrevision.com a Compiled by Mr. Lafferty Maths Dept.

  10. Pythagoras’s Theorem x www.mathsrevision.com y z Compiled by Mr. Lafferty Maths Dept.

  11. Summary of Pythagoras’s Theorem www.mathsrevision.com Note: The equation is ONLY valid for right-angled triangles. Compiled by Mr. Lafferty Maths Dept.

  12. S3 Credit Calculating Hypotenuse Learning Intention Success Criteria • Know the term hypotenuse “ the longest side” • Use Pythagoras Theorem to calculate the length of the hypotenuse • “the longest side” • Use Pythagoras Theorem to calculate the hypotenuse. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  13. S3 Credit Two key points when dealing with right-angled triangles Calculating Hypotenuse The longest side in a right-angled triangle is called The HYPOTENUSE The HYPOTENUSE is ALWAYS opposite the right angle www.mathsrevision.com x (xz)2 = (xy)2 + (yz)2 c2 = a2 + b2 c b z y a Compiled by Mr. Lafferty Maths Dept.

  14. Calculating the Hypotenuse Example 1 Q2. Calculate the longest length of the right- angled triangle below. c 8 www.mathsrevision.com 12 Compiled by Mr. Lafferty Maths Dept.

  15. Calculating the Hypotenuse Example 2 Q1. 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? A www.mathsrevision.com LA = 8 G L GL =15 Airport Lennoxtown Compiled by Mr. Lafferty Maths Dept.

  16. Calculating Hypotenuse S3 Credit Now try Ex 2.1 and 2.2 MIA Page 147 www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  17. S3 Credit S3 Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  18. S3 Credit Length of the smaller side Learning Intention Success Criteria • Use Pythagoras Theorem to find the length of smaller side. 1. To show how Pythagoras Theorem can be used to find the length of the smaller side. • 2. Show all working. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  19. Length of the smaller side 20cm 12cm a cm S3 Credit 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.

  20. Length of the smaller side 10cm b cm 8 cm S3 Credit Example : Find the length of side a ? www.mathsrevision.com Check answer ! Always smaller than hypotenuse Compiled by Mr. Lafferty Maths Dept.

  21. N G H O C D E F M P L K P(x,y) r I J o A A Q R U V C T B W Z S

  22. Length of smaller side S3 Credit Now work through Ex3.1 and Ex 3.2 Odd Numbers Only www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  23. S3 Credit S3 Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  24. S3 Credit Solving Real – Life ProblemsUsing Pythagoras Theorem Learning Intention Success Criteria • Apply Pythagoras Theorem to solve real-life problems. 1. To show how Pythagoras Theorem can be used to solve real-life problems. • 2. Show all working. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  25. Solving Real-Life Problems 17m rod 8m S3 Credit 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 height of the tree ? www.mathsrevision.com a c b Compiled by Mr. Lafferty Maths Dept.

  26. Solving Real-Life Problems S3 Credit Example 2 A garden has a fence around its perimeter and along its diagonal as shown below. What is the length of the fence from D to C. A B www.mathsrevision.com 13m 5m D C b m Compiled by Mr. Lafferty Maths Dept.

  27. Length of smaller side S3 Credit Now work through Ex4.1 and Ex 4.2 Odd Numbers Only www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  28. S3 Credit S3 Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  29. S3 Credit Pythagoras TheoremTwice Learning Intention Success Criteria • Use the appropriate form of Pythagoras Theorem to solving harder problems. 1. To use knowledge already gained on Pythagoras Theorem to solve harder problems using Theorem twice. • 2. Show all working. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  30. Solving Real-Life Problems S3 Credit Problem : Find the length of h. Find length BD first h B C 15 www.mathsrevision.com 12 A D 13

  31. Solving Real-Life Problems S3 Credit Problem : Find the length of length y. Now find h h B C 15 www.mathsrevision.com 12 A D 13

  32. Solving Real-Life Problems S3 Credit Problem : Find the diagonal length of the cuboid AG. Find AH first F G B C 7cm www.mathsrevision.com E H 10cm 6cm A D 8cm

  33. Solving Real-Life Problems S3 Credit Problem : Find the diagonal length of the cuboid AG. Now find AG F G B C 7cm www.mathsrevision.com E H 10cm 6cm A D 8cm

  34. Pythagoras Theorem S3 Credit Now try Ex 5.1 Ch8 (page 154) www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  35. S3 Credit S3 Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  36. S3 Credit Converse of Pythagoras Theorem Learning Intention Success Criteria • Apply the converse of Pythagoras Theorem to prove a triangle is • right-angled. 1. To explain the converse of Pythagoras Theorem to prove a triangle is right-angled. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  37. Converse1 – talk Converse2 – opposite, reverse Converse of Pythagoras Theorem S3 Credit c Converse Theorem states that if b a 1. Then triangle MUST be right-angled. www.mathsrevision.com 2. Right-angle is directly opposite C. Hypotenuse Compiled by Mr. Lafferty Maths Dept.

  38. Converse of Pythagoras Theorem S3 Credit Problem : Is this triangle right-angled ? Explain Answer If it is then Pythagoras Theorem will be true 10cm 6 cm www.mathsrevision.com 9 cm By the Converse Theorem, triangle is NOT right-angled Compiled by Mr. Lafferty Maths Dept.

  39. Converse of Pythagoras Theorem S3 Credit Problem : A picture frame manufacturer claims that his are rectangular is his claim true. If it is then Pythagoras Theorem will be true 50cm 40 cm www.mathsrevision.com 30 cm By the Converse Theorem, frame IS rectangular Compiled by Mr. Lafferty Maths Dept.

  40. Converse of Pythagoras Theorem S3 Credit Now try Ex 6.1 & 6.2 Ch8 (page 156) www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

More Related