Plane Geometry · 69 lessons

An angle chase starts with a few angles you know and works out the rest without measuring. Nearly every rule comes from two facts: angles on a straight line add to 180°, and a line crossing two parallel lines makes the same angles at both crossings.

1. 1Circles, Triangles, Squares and Rectangles
2. 2Half Circles and Quarter Circles
3. 3Shapes Turned and Resized
4. 4Above, Below and Beside
5. 5Counting Sides and Corners
6. 6Making Shapes from Smaller Shapes
7. 7Continuing a Shape Pattern
8. 8Copying a Figure on a Grid
9. 9Drawing Rectangles and Squares
10. Building with shapes (11)
11. 10Angles
12. 11Measuring and Drawing Angles
13. 12Symmetry
14. 13Completing a Symmetric Figure
15. Symmetry and grids (11)
16. 14Area of a Triangle
17. 15Area of a Parallelogram
18. 16Area of a Trapezium
19. 17Area of a Composite Figure
20. Composite areas (12)
21. Overlapping shapes (10)
22. 18Circumference and Diameter
23. 19Area of a Circle
24. 20Pythagoras’ Theorem
25. 21Proving Pythagoras by Dissection
26. 22Finding a Shorter Side with Pythagoras’ Theorem
27. 23The Converse of Pythagoras’ Theorem
28. 24Similar Shapes
29. 25Finding Similar Triangles in a Figure
30. Pythagoras and similar shapes (10)
31. 26Angles at a Point
32. 27Angles on a Line
33. 28Complementary Angles
34. 29Vertically Opposite Angles
35. 30Parallel and Perpendicular Lines
36. 31Drawing Parallel and Perpendicular Lines
37. 32Angles in Parallel Lines
38. 33Angles in a Triangle
39. 34Angles in a Polygon
40. 35The Interior Angle of a Regular Polygon
41. 36Constructing a Perpendicular Bisector
42. 37Constructing an Angle Bisector
43. 38Constructing a Perpendicular from a Point
44. 39Constructing a Triangle
45. 40Loci
46. 41Triangles on a Sphere Break the 180 Rule
47. 42Why an Angle Cannot Be Trisected
48. 43Angle Chases
49. Angles and lines (11)
50. Triangles (10)
51. Constructions and Loci (11)
52. 44Special Quadrilaterals
53. 45Rhombus and Kite
54. 46Area of Composite Shapes
55. 47Plans and Elevations
56. 48Congruence Tests
57. 49Similarity Conditions
58. 50The Midpoint Theorem
59. 51Ratio of Areas
60. 52Ratio of Volumes
61. 53Angle in a Semicircle
62. 54Chords, Arcs, Sectors and Segments
63. 55Arcs and Sectors
64. 56The Area of a Segment
65. 57Angle at the Center
66. 58Angles in the Same Segment
67. 59Cyclic Quadrilaterals
68. 60Tangent Properties
69. 61The Alternate Segment Theorem
70. 62Chords and the Center
71. 63Circle Theorems with Algebra
72. Congruence, Similarity and Circle Theorems (12)
73. 64Reflection
74. 65Rotation
75. 66Translation of Shapes
76. 67Enlargement with a Center
77. 68Combined Transformations
78. 69Rotational Symmetry
79. Paper folding (10)
80. Transformations (10)