1. © T Madas

2. P a r a l l e l l i n e s n e v e r m e e t What are parallel lines? Parallel lines stay the same distance apart

3. © T Madas What are perpendicular lines? Perpendicular lines are lines at right angles with each other

4. © T Madas Transversal 1 2 3 4 6 5 7 8 Vertically Opposite Angles Vertically Opposite Angles are EQUAL

5. © T Madas Transversal 1 2 3 4 6 5 7 8 Corresponding Angles Corresponding Angles are EQUAL

6. © T Madas Transversal 1 2 3 4 6 5 7 8 Alternate Angles or Z -angles Alternate Angles are EQUAL

7. © T Madas Recognising these Special Angles

8. Which angle is vertically opposite to angle a ? Which is the corresponding angle to angle a ? a 1 2 3 4 5 6 7 Which angle is vertically opposite to angle k ? Which is the corresponding angle to angle k ? k 5 7 2 4 1 6 3

9. Which is the corresponding angle to angle n ? Which angle is alternate angle to angle n ? n 1 6 3 2 5 4 7 Which angle is vertically opposite to angle p ? Which is the alternate angle to angle p ? p 5 4 2 7 1 6 3

10. t 1 2 3 4 5 6 7 Which angle is vertically opposite to angle t ? Which is the corresponding angle to angle t ? Which is the corresponding angle to angle q ? Which angle is alternate angle to angle q ? q 2 7 3 1 4 5 6

11. b 1 2 3 4 5 6 7 Which angle is vertically opposite to angle b ? Which is the corresponding angle to angle b ? Which is the corresponding angle to angle h ? Which angle is alternate angle to angle h ? h 6 1 5 7 4 3 2

12. Which angle is alternate angle to angle x ? Which are the corresponding angles to angle x ? x 1 3 2 8 9 10 11 4 5 7 12 13 14 15 6

13. © T Madas Which angle is alternate angle to angle x ? Which are the corresponding angles to angle x ? x 1 3 2 8 9 10 11 4 5 6 7 12 13 14 15

14. © T Madas Which angle is alternate angle to angle x ? Which are the corresponding angles to angle x ? x 1 3 2 8 9 10 11 4 5 6 7 12 13 14 15

15. © T Madas Which angle is alternate angle to angle x ? Which are the corresponding angles to angle x ? x 1 3 2 8 9 10 11 4 5 6 7 12 13 14 15

16. © T Madas Some Practice

17. © T Madas 70° ? 50°

18. © T Madas ? One of the many solutions: 70° 50° 70° 50° 70° 60° 70° 50° Vertically Opposite Alternate angles Corresponding angles Vertically Opposite Angles in a triangle Vertically opposite

19. © T Madas One of the many solutions: 70° 50° 70° 50° How can we find this angle in one quick Step from this position?

20. © T Madas One of the many solutions: 70° 50° 70° 50°

21. © T Madas More Practice

22. © T Madas 62° 118° 62° straight line corresponding vertically opposite

23. © T Madas straight line 62° 118° corresponding

24. © T Madas 48° 56° 48° 56° vertically opposite alternate OR corresponding

25. © T Madas 41° 54° 41° alternate corresponding

26. © T Madas 46° 47° 134° 47° 134° alternate straight line corresponding

27. © T Madas 52° 38° vertically opposite angles in a triangle alternate

28. © T Madas

29. 2x2x 3x3x 2x2x Find the value of x and hence calculate these two angles Alternate Angles Straight Line 3x3x+2x2x=180° c 5x5x= c x=36° 72° 108°

30. © T Madas 100° Find the value of the angle marked in purple 52° 48° 52° 48°

31. © T Madas Find the value of the angle marked in purple 27° 58° 27° 58° 275°

32. © T Madas Find the value of the angle marked in purple 125° 105° 75° 55° 50°

33. © T Madas Find the value of x and hence calculate these two angles 2x2x 3x3x 2x2x 3x3x+2x2x=90° c 5x5x= c x=18°

34. © T Madas Find the value of x and hence calculate these two angles 3x3x+2x2x=90° c 5x5x= c x=18° 36° 54°

35. © T Madas Find the value of angle x ONLY x a a b b 2a2a 2a2a+2b2b=180° c a+b=90°

36. © T Madas

37. A farm gate consists of three parallel planks of wood with a metal bar running diagonally for extra support, as shown in the diagram. Calculate the angles x, y and z. 30° y x z x and the 30° angle are ALTERNATE ANGLES x =x =30°

38. © T Madas A farm gate consists of three parallel planks of wood with a metal bar running diagonally for extra support, as shown in the diagram. Calculate the angles x, y and z. 30° y x z x =x = y =y = y and the 30° angle are CORRESPONDING ANGLES

39. © T Madas A farm gate consists of three parallel planks of wood with a metal bar running diagonally for extra support, as shown in the diagram. Calculate the angles x, y and z. 30° y x z x =x = y =y = z =z = 150° ALTERNATE ANGLES 30°

40. © T Madas

41. A B C D E 25° 55° ABCD is a trapezium R ADB = 90° R DBE = 25° and R EBC = 55° 1. Calculate R ABD 2. Calculate R DAB 3. Calculate R BDC

42. © T Madas A C D E 25° 55° ABCD is a trapezium R ADB = 90° R DBE = 25° and R EBC = 55° 1. Calculate R ABD 2. Calculate R DAB 3. Calculate R BDC B 30° 60° Alternate Angles Angles of a triangle

43. © T Madas A C D E 25° 55° ABCD is a trapezium R ADB = 90° R DBE = 25° and R EBC = 55° 1. Calculate R ABD 2. Calculate R DAB 3. Calculate R BDC B 30° 60° 30° Alternate Angles

44. © T Madas