1. 4-Aug-15Created by Mr.Lafferty Math Dept Revising Basic Angles Naming Angles www.mathsrevision.com Finding Missing angles Angles in a Triangle Corresponding Angles Alternate Angles Angles National 4 REL 1.2c Angles in a Quadrilateral Drawing Triangles Measuring Angles

2. 4-Aug-15Created by Mr.Lafferty Math Dept Starter Questions Q3.Calculate 2.34 + 4.7 + 0.12 Q1.Convert to the 24 hour clock. (a)7:25 pm (b)6:50 am Q2.Write down the type of angle that is less than 90 deg. Q4.Round the following to nearest 1000. (a)12,501(b)369,765 www.mathsrevision.com National 4 REL 1.2c

3. 4-Aug-15Created by Mr.Lafferty Math Dept Learning Intention Success Criteria 1.To be able to identify acute, right-angle, obtuse, straight line and reflex angles. 1.To revise Type of Angles. www.mathsrevision.com Type of Angles National 4 REL 1.2c

4. 4-Aug-15Created by Mr.Lafferty Math Dept Acute less than 90 o Obtuse Between 90 o – 180 o Right Angle exactly 90 o reflex over 180 o less than 360 o www.mathsrevision.com Straight Line Angle exactly 180 o Type of Angles Horizontal Vertical National 4 REL 1.2c

5. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ch2 (page 14) Exercise 1 www.mathsrevision.com Type of Angles National 4 REL 1.2c

6. 4-Aug-15Created by Mr.Lafferty Math Dept Starter Questions www.mathsrevision.com Q3.Calculate 5.65 – 1.3 Q1.Convert to the 12 hour clock. (a)17:15 (b)05:40 Q2.Write down 2 numbers that add to give 8 and multiply to give 15. Q4.Round the following to nearest 100. (a)13,551(b)369,449 National 4 REL 1.2c

7. 4-Aug-15Created by Mr.Lafferty Math Dept Learning Intention Success Criteria 1.To be able to name an angle. 1.To explain how we name angles by THREE capital letters with the angle sign. The middle letter being where the angle is. 2.Understand the difference between the type of angle and the name of an angle. www.mathsrevision.com Naming Angles National 4 REL 1.2c

8. 4-Aug-15Created by Mr.Lafferty Math Dept Naming Angles www.mathsrevision.com A B C Type of angle is acute Name of angle is ∠ ABC Type of angle is obtuse Name of angle is ∠ ZYX X Y Z MIDDLE LETTER IS ALWAYS WHERE THE ANGLE IS ALWAYS 3 CAPITAL LETTERS National 4 REL 1.2c

9. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ch2 (page 15) Exercise 2 www.mathsrevision.com Naming Angles National 4 REL 1.2c

10. 4-Aug-15Created by Mr. Lafferty10 Starter Questions Q3.List the prime numbers between 10 and 20. Q1.Convert to the 12 hour clock. (a)17:15 (b)05:40 Q2.Write down lowest common multiple of 3, 4, 5. Q4.Round the following to nearest 100. (a)13,551(b)369,449

11. 4-Aug-1511 A 180 o Protractor Outside scale from 0 o to 180 o going in a clockwise direction. Inside scale from 0 o to 180 o going in an anti-clockwise direction.

12. 4-Aug-1512 You need to be able to measure an angle to the nearest degree. To help you do this you should always: 1. Look directly down onto the cross point. 2. Always use the protractor in a horizontal manner as shown below.

13. 4-Aug-1513 1 2 Measuring Angles with a 180 o Protractor 0 on the outside so use outside scale 0 on the inside so use inside scale 67 o 50 o

14. 4-Aug-1514 3 4 Measuring Angles with a 180 o Protractor 0 on the outside so use outside scale 0 on the inside so use inside scale 135 o 120 o

15. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ch2 (page 17) Exercise 3 www.mathsrevision.com Naming Angles National 4 REL 1.2c

16. 4-Aug-15Created by Mr.Lafferty Math Dept Starter Questions www.mathsrevision.com National 4 REL 1.2c

17. 4-Aug-15Created by Mr.Lafferty Math Dept Learning Intention Success Criteria 1.To know 360 o in a circle. 1.To calculate missing angle give all other angles. 2.Find missing angle given all other angles. www.mathsrevision.com Find Missing Angles National 4 REL 1.2c

18. 4-Aug-15Created by Mr.Lafferty Math Dept 120 o 95 o Find Missing Angle www.mathsrevision.com Angles round a point always add up to 360 o 65 o Two angles making a straight line add up to 180 o (Supplementary angles) Angles opposite each other at a cross are equal. 34 o 115 o 146 o 146 o 145 o 35 o Two angles making a right angle add up to 90 o (Complementary angles) 55 o National 4 REL 1.2c

19. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Created by Mr Lafferty 19 x 47 o 1 114 o y 2 3 4 76 o a 82 o b Angle x = 180 – 47 = 133 o Angle y = 180 – 114 = 66 o Angle a = 180 – 76 = 104 o Angle b = 180 – 82 = 98 o www.mathrevision.com Angles and Triangles National 4 REL 1.2c

20. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Created by Mr Lafferty 20 Angle x o = 360 o - (90 o + 100 o + 105 o ) 90 100 105 + 295 Example Find angle x. 360 o 105 o 100 o xoxo Think ! www.mathsrevision.com Angles and Triangles = 360 o – 295 o = 65 o National 4 REL 1.2c

21. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ch2 (page 20) Exercise 4 www.mathsrevision.com Find Missing Angle National 4 REL 1.2c

22. 4-Aug-15Created by Mr. Lafferty22 (SAS) Starter Questions Q3.Calculate the missing angles. 80 o Q1.Convert the percentages to fractions. (a)30%(b)60% Q2.Write down all the factors of 16. Q4.Round the following to 1 decimal place. (a)4.549(b)6.551

23. 4-Aug-15Created by Mr. Lafferty23 Drawing SAS Triangles SAS Triangles Angle Side Side

24. 4-Aug-15Created by Mr. Lafferty24 Drawing SAS Triangles Toolkit required 1.Ruler 2.Protractor 3.Pencil & Paper

25. 4-Aug-15Created by Mr. Lafferty25 Drawing SAS Triangles Example : Draw to scale the triangle ABC with AB = 6cm and angle CAB = 30 o and AC = 5cm Step 1Draw line AB=6cm AB C Step 2Measure angle CAB from A Step 3Draw the line AC = 5cm through X. Label it C. Step 4Join C to B. Check angles add to 180 o A B C 30 o X

26. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ch2 (page 22) Exercise 5 www.mathsrevision.com Find Missing Angle National 4 REL 1.2c

27. 4-Aug-15Created by Mr.Lafferty Math Dept Starter Questions www.mathsrevision.com 75 o xoxo National 4 REL 1.2c

28. 4-Aug-15Created by Mr.Lafferty Math Dept Sum of Angles in a Triangle Learning Intention Success Criteria 1.To know all angles in a triangle add to 180 o. 1.To show that all the angles in a triangle sum to 180 o. 2.Use knowledge to solve problems. www.mathsrevision.com National 4 REL 1.2c

29. 4-Aug-15Created by Mr.Lafferty Math Dept To determine the angle sum of any Triangle Cut off corners  www.mathsrevision.com National 4 REL 1.2c

30. 4-Aug-15Created by Mr.Lafferty Math Dept angle sum of any Triangle All angles in a triangle ALWAYS added up to180 o 180 o www.mathsrevision.com National REL 1.2c

31. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Created by Mr Lafferty 31 Equilateral TriangleIsosceles triangleRight-angled triangle Angles and Triangles www.mathsrevision.com 3 equal sides 3 equal angles. 2 equal sides 2 equal angles (base) One angle is 90 o National 4 REL 1.2c

32. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Created by Mr Lafferty 32 Example 1 a 65 o Calculate angle a. Angle a = 180 – (90 + 65) = 180 – 155 = 25 o Example 2 Calculate angles a, b and c a b c Since the triangle is equilateral, angles a, b and c are all 60 o (180/3) Angles and Triangles www.mathsrevision.com National 4 REL 1.2c

33. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Created by Mr Lafferty 33 Angle a = 65 o (base angles of an isosceles triangle are equal). a 65 o Example 3 Calculate angle a. b Angle b = 180 –(65 + 65) = 180 – 130 = 50 o Example 4 Calculate angles x and y y 130 o x Angles and Triangles www.mathsrevision.com National 4 REL 1.2c

34. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Created by Mr Lafferty 34 Example 5 Calculate angles a and b. b a Angles and Triangles www.mathsrevision.com Isosceles triangle National 4 REL 1.2c

35. 4-Aug-15Created by Mr.Lafferty Math Dept Sum of Angles in a Triangle www.mathsrevision.com Copy out the following triangles and find the missing angles. 32 o 50 o 38 o 87 o xoxo xoxo xoxo xoxo Remember all the angles add up to 180 o National 4 REL 1.2c

36. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ex 6 Ch2 (page 23) www.mathsrevision.com Sum of Angles in a Triangle National 4 REL 1.2c

37. 4-Aug-15Created by Mr.Lafferty Math Dept Starter Questions Q1.Solve the equation below Q2.Find two numbers that multiply to give 18 and subtract to give 3. Q3.Find the average and range of the numbers below Q4.Find 2,8,8,10 www.mathsrevision.com National 4 REL 1.2c

38. 4-Aug-15Created by Mr.Lafferty Math Dept www.mathsrevision.com Learning Intention Success Criteria 1.To understand the term corresponding angles. 1. To explain the term corresponding angles and show how we use the property to solve problems. 2. To be able to use property to solve problems. Angles Corresponding Angles National 4 REL 1.2c

39. 4-Aug-15Created by Mr.Lafferty Math Dept www.mathsrevision.com Angles Corresponding Angles Which angles are equal? National 4 REL 1.2c

40. 4-Aug-15Created by Mr.Lafferty Math Dept www.mathsrevision.com Angles Corresponding Angles Which angles are equal? National 4 REL 1.2c

41. 4-Aug-15Created by Mr.Lafferty Math Dept www.mathsrevision.com Angles Corresponding Angles Which angles are equal to the shaded angle? National 4 REL 1.2c

42. 4-Aug-15Created by Mr.Lafferty Math Dept www.mathsrevision.com Angles Which angles are equal to the shaded angle? National 4 REL 1.2c

43. 4-Aug-15Created by Mr.Lafferty Math Dept look for shapes www.mathsrevision.com Angles Corresponding Angles National 4 REL 1.2c

44. 4-Aug-15Created by Mr.Lafferty Math Dept 120 x www.mathsrevision.com Angles What is the value of letter x? Corresponding Angles National 4 REL 1.2c

45. 4-Aug-15Created by Mr.Lafferty Math Dept 100 a www.mathsrevision.com Angles What is the value of letter a? Corresponding Angles National 4 REL 1.2c

46. 4-Aug-15Created by Mr.Lafferty Math Dept 48 b www.mathsrevision.com Angles What is the value of letter b? Corresponding Angles National 4 REL 1.2c

47. 4-Aug-15Created by Mr.Lafferty Math Dept 110 c www.mathsrevision.com Angles What is the value of letter c? Corresponding Angles National 4 REL 1.2c

48. 4-Aug-15Created by Mr.Lafferty Math Dept 70 a b 110 What are the values of letters a and b? www.mathsrevision.com Angles Corresponding Angles National 4 REL 1.2c

49. 4-Aug-15Created by Mr.Lafferty Math Dept 115 65 115 65 What are the values of the missing angles? www.mathsrevision.com Angles Corresponding Angles National 4 REL 1.2c

50. 4-Aug-15Created by Mr.Lafferty Math Dept 57 123 57 123 What are the values of the missing angles? www.mathsrevision.com Angles Corresponding Angles National 4 REL 1.2c

51. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ch2 Extension Booklet Ex7E Page 1 Q1 to Q4 www.mathsrevision.com Angles Corresponding Angles National 4 REL 1.2c

52. 4-Aug-15Created by Mr.Lafferty Math Dept Starter Questions Q1.Solve the equation below Q2.Find two numbers that multiply to give 48 and divide to give 3. Q3.Find missing angles 119 o aoao bobo www.mathsrevision.com National 4 REL 1.2c

53. 4-Aug-15Created by Mr.Lafferty Math Dept www.mathsrevision.com Learning Intention Success Criteria 1.To understand the term alternate angles. 1. To explain the term alternate angles and show how we use the property to solve problems. 2. To be able to use property to solve problems. Angles Alternate Angles National 4 REL 1.2c

54. 4-Aug-15Created by Mr.Lafferty Math Dept Look for - Z shapes www.mathsrevision.com Angles Alternate Angles = equal angles National 4 REL 1.2c

55. 4-Aug-15Created by Mr.Lafferty Math Dept 35 a www.mathsrevision.com Angles Alternate Angles Find the value of a ? National 4 REL 1.2c

56. 4-Aug-15Created by Mr.Lafferty Math Dept b 43 www.mathsrevision.com Angles Alternate Angles Find the value of b ? National 4 REL 1.2c

57. 4-Aug-15Created by Mr.Lafferty Math Dept 33 c www.mathsrevision.com Angles Alternate Angles Find the value of c ? National 4 REL 1.2c

58. 4-Aug-15Created by Mr.Lafferty Math Dept 123 d www.mathsrevision.com Angles Alternate Angles Find the value of d ? National 4 REL 1.2c

59. 4-Aug-15Created by Mr.Lafferty Math Dept 50 a b13050 www.mathsrevision.com Angles Alternate Angles Find the value a and b ? National 4 REL 1.2c

60. 4-Aug-15Created by Mr.Lafferty Math Dept 135 c 45 d www.mathsrevision.com Angles Alternate Angles Find the value of a and b ? National 4 REL 1.2c

61. 4-Aug-15Created by Mr.Lafferty Math Dept 60 a b c120 60120 www.mathsrevision.com Angles Alternate Angles Find the value a, b and c ? National 4 REL 1.2c

62. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ch2 Extension Booklet Ex7E Page 4 Q5 to Q7 www.mathsrevision.com Angles Alternate Angles National 4 REL 1.2c

63. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015 63 Created by Mr.Lafferty Q3.Express the following percentages as fractions Starter Questions Q1.List 4 properties of a square. Q2.Simplify the following fraction Q4.Solve www.mathsrevision.com National 4 REL 1.2c

64. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015 Angles in a Quadrilateral IMPORTANT : The angles in a quadrilateral ALWAYS add up to 360 o C D A B We have split the quadrilateral into two triangles But for any triangle the sum of the angles is 180 0 Hence for the quadrilateral we have 2 x 180 o =360 o aoao coco bobo dodo www.mathsrevision.com National 4 REL 1.2c

65. Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015Tuesday, 04 August 2015 65 Created by Mr.Lafferty Angles in a Quadrilateral Question : Find the missing angle below. x y z w 34 o 100 o The four angles of a quadrilateral add to = 360 o yoyo www.mathsrevision.com National 4 REL 1.2c

66. 4-Aug-15Created by Mr.Lafferty Math Dept Now try Ch2 Extension Booklet Ex8E Page 7 www.mathsrevision.com Angles Angles in a Quadrilateral National 4 REL 1.2c