1. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem www.mathsrevision.com Squaring a Number and Square Roots Investigating Pythagoras Theorem Finding the length of the smaller side Mixed problems Calculating the Hypotenuse Solving real-life problems Distance between two points

2. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com

3. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Squaring a Number www.mathsrevision.com Learning Intention Success Criteria 1.To understand what is meant by the term ‘squaring a number’ 1.To understand the term ‘squaring a number’. 2.Be able to calculate squares both mentally and using the calculator.

4. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. www.mathsrevision.com Squaring a Number To square a number means to : “Multiply it by itself” means 9 x 9 = 81 Example : means 10 x 10 = 100

5. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Now try Exercise 1 Ch13 (page 151) www.mathsrevision.com Squaring a Number

6. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. www.mathsrevision.com Square Root of a number You now know how to find : We can ‘undo’ this by asking “which number, times itself, gives 81” 9 2 = 9 x 9 = 81 From the top line, the answer is 9 This is expressed as : “ ““ “the SQUARE ROOT of 81 is 9” or in symbols we write :

7. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Now try Exercise 2 Ch13 (page 153) www.mathsrevision.com Square Root of a Number

8. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Starter Questions Q1.Are the missing angles 65 o, 40 o and 65 o Q2.Calculate Q3. The cost of a new computer is £1000 +vat. If the vat is charged at 12% what is the total cost. Q4. The cost of a bag of sugar is £1.12. How much 50 bags cost. 115 o NON-CALCULATOR www.mathsrevision.com

9. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. ‘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. ‘ Aim of today's Lesson Right – Angle Triangles www.mathsrevision.com

10. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Right – Angle Triangles What is the length of a ? What is the length of b ? Copy the triangle into your jotter and measure the length of c 3 4 5 www.mathsrevision.com

11. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Right – Angle Triangles What is the length of a ? What is the length of b ? Copy the triangle into your jotter and measure the length of c 6 8 10 www.mathsrevision.com

12. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Right – Angle Triangles What is the length of a ? What is the length of b ? Copy the triangle into your jotter and measure the length of c 5 12 13 www.mathsrevision.com

13. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Right – Angle Triangles abca2a2 b2b2 c2c2 345 51213 6810 Copy the table below and fill in the values that are missing www.mathsrevision.com

14. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Right – Angle Triangles abca2a2 b2b2 c2c2 34591625 5121325144169 68103664100 Can anyone spot a relationship between a 2, b 2, c 2. www.mathsrevision.com

15. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Pythagoras’s Theorem a b c www.mathsrevision.com

16. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Summary of Pythagoras’s Theorem Note: The equation is ONLY valid for right-angled triangles. www.mathsrevision.com

17. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch13 (page 154) Pythagoras Theorem www.mathsrevision.com

18. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com

19. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Calculating Hypotenuse www.mathsrevision.com Learning IntentionSuccess Criteria 1.Know the term hypotenuse “ the longest side” 1.Use Pythagoras Theorem to calculate the length of the hypotenuse “the longest side” 2.Use Pythagoras Theorem to calculate the hypotenuse.

20. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Calculating the Hypotenuse 8 12 c Q2.Calculate the longest length of the right- angled triangle below. www.mathsrevision.com Example 1

21. National 4 REL 1.2a 4-Aug-15 Compiled by Mr. Lafferty Maths Dept. Calculating the Hypotenuse Aeroplane b = 8 a = 15 c Lennoxtown Airport 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? www.mathsrevision.com Example 2

22. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Now try Exercise 4 Ch13 (page 156) Calculating Hypotenuse www.mathsrevision.com

23. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com

24. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Solving Real-Life Problems www.mathsrevision.com Learning Intention Success Criteria 1.Solve real-life problems using Pythagoras Theorem. 1.To show how Pythagoras Theorem can be used to solve real-life problems.

25. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Solving Real-Life Problems Example :A steel rod is used to support a tree which is in danger of falling down. What is the length of the rod? 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. www.mathsrevision.com 15m 8m rod

26. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. 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

27. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Now try Exercise 5 Ch13 (page 159) Solving Real-Life Problems www.mathsrevision.com

28. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com

29. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Length of the smaller side www.mathsrevision.com Learning Intention Success Criteria 1.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.

30. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Length of the smaller side Example :Find the length of side a ? To find the length of the smaller side of a right- angled triangle we simply rearrange Pythagoras Theorem. www.mathsrevision.com 20cm 12cm a cm Check answer ! Always smaller than hypotenuse

31. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Length of the smaller side Example :Find the length of side b ? www.mathsrevision.com 10cm b cm 8 cm Check answer ! Always smaller than hypotenuse

32. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Now try Exercise 6 Ch13 (page 161) Length of smaller side www.mathsrevision.com

33. National 4 REL 1.2a Starter Questions www.mathsrevision.com ALWAYS comes up in exam !!

34. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Apply Pythagoras Theorem to find length of a line. 1.To show how Pythagoras Theorem can be used to find the length of a line. 2.Show all working. Finding the Finding the Length of a Line

35. National 4 REL 1.2a 4-Aug-15 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 13240 1 3 2 5 4 6 5768910 7 8 (7,7) (2,4) 3 5 Finding the Length of a Line Discuss with your partner how we might find the length of the line.

36. 4-Aug-15 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 13240 1 3 2 5 4 6 5768910 7 8 (9,1) (0,6) 5 9 Pythagoras Theorem to find the length of a Line National 4 REL 1.2a

37. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Now try Extension Booklet Pythagoras Theorem to find the length of a Line www.mathsrevision.com

38. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com

39. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem www.mathsrevision.com Learning Intention Success Criteria 1.Use the appropriate form Pythagoras Theorem to solving problems. 1.To use knowledge already gained on Pythagoras Theorem to solve mixed problems using appropriate version of Theorem.

40. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem www.mathsrevision.com Finding hypotenuse c Finding shorter side a Finding shorter side b a c b

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42. National 4 REL 1.2a 4-Aug-15Compiled by Mr. Lafferty Maths Dept. Now try Extension Booklet Pythagoras Theorem www.mathsrevision.com