1. Geometric Reasoning
Mahobe

2. The facts to learn

3. Angles in a triangle add up to 180o

4. Angles on a straight line add up to 180o

5. Angles around a point add up to 360o

9. base ∠’s isos ∆ =

11. ∠ sum quad
Interior angles of a quadrilateral sum to 360o

12. opp ∠, cyclic quad
Opposite angles of a cyclic quadrilateral sum to 180o

13. Ext ∠, of cyclic quad
Exterior angle of a cyclic quad equals the opposite interior angle

14. vert opp ∠s =
Vertically opposite angles are equal

15. alt ∠s // lines
Alternate angles are equal if the lines are parallel

16. corr ∠s // lines
Corresponding angles are equal if the lines are parallel

17. Co-int ∠s // lines
Co-interior angles sum to 180o if the lines are parallel

18. Exterior angles of a polygon add up to 360o

19. If the polygon is regular all exterior angles are the same size
Exterior angles of a polygon add up to 360o

20. ext ∠ regular pentagon
Exterior angles of a regular pentagon is 72o

21. Interior angles of a polygon with n sides sum to 180(n-2)

22. Find all the other angles in this figure

30. Vert opp angles

33. A triangle formed with 2 radii is isosceles

37. The angle at the centre is twice the angle at the circumference.

38. When writing angles use 3 letters
When writing angles use 3 letters. The middle letter is where the angle is.

39. Find the angles u, v and w
O Is the centre

40. O Is the centre

41. O Is the centre

42. O Is the centre

43. Find angle d

46. Calculate the size of angle ABC

52. Calculate angle CDE

54. Calculate the size of angle HIJ

56. Calculate the size of angle c

57. C = 96o, Co-int angle // lines Corr angles // lines OR
Angles on a line
Opp angles parallelogram

58. Calculate the size of angle VUW

60. Shape P is a regular pentagon and shape H is a regular heptagon
Shape P is a regular pentagon and shape H is a regular heptagon. Calculate the size of angle CBD

61. Shape P is a regular pentagon and shape H is a regular heptagon
Shape P is a regular pentagon and shape H is a regular heptagon. Calculate the size of angle CBD

62. The diagram gives the angles of a playground slide. Find angle XYZ.

64. Find the size of angles NMO and OPN

65. Find the size of angles NMO and OPN

66. Find the size of angles PRQ and PSQ

67. O

70. XBC 90
Rad perp. tang
CBA 20
Angles on a line
CAB
Base angles isos triangle
XCB 40
Ext angle = sum opp int angles
CXB 50
Angle sum triangle

73. O Is the centre of the circle. Calculate the size of angle BCD

75. O Is the centre of the circle. Calculate the size of angle WYX

78. Similar triangles

79. ABC is an isosceles triangle. O is the centre of the circle
ABC is an isosceles triangle. O is the centre of the circle. Calculate the size of angles BAC and ODC

82. Calculate the size of angles x and y.

83. .

84. O is the centre of the circle. Calculate the size of angle BAC.

85. .

87. KNML is cyclic as the opposite angles sum to 180.

88. O is the centre of the circle. Prove angle CBY = angle CAB

89. angle CBY = angle CAB