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Geometric Reasoning

Geometric Reasoning. Types of Angles. Polygons. A Polygon is a closed figure made up of straight sides. They are given special names when we know the number of sides. Polygons. A regular polygon is one that has all its sides and angles the same. An irregular polygon does not.

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Geometric Reasoning

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  1. Geometric Reasoning

  2. Types of Angles

  3. Polygons • A Polygon is a closed figure made up of straight sides. They are given special names when we know the number of sides.

  4. Polygons • A regular polygon is one that has all its sides and angles the same. An irregular polygon does not. • Examples of regular polygons

  5. Types of Triangles

  6. Types of Quadrilaterals • There are several quadrilaterals including Square, Rectangle, Parallelogram, Rhombus. • Quadrilaterals are a type of polygon with four sides, and four angles adding up to 360°. A pushed over square A pushed over rectangle

  7. Exterior Angles of Polygons • This is easy, they add up to 360°. Think of the opening of a camera. As it gets smaller and smaller it comes to a point. (360º)

  8. Interior Angles of Polygons • The formula for calculating the sum of the interior angles of a regular polygon is: • 
(n - 2) × 180° where n is the number of sides of the polygon.

  9. Interior angle of a regular polygon Example: • Find the interior angle of a regular hexagon. • You know that the interior angles of a hexagon add up to 720°
As a hexagon has six sides, each angle is equal to = 120°.

  10. N 0700 Bearings • Bearings are special angles that give directions. They are measured clockwise from North, and are always written using three digits. • EG:

  11. Exercises • Types of angles: • Exercise 9.3 All • Bearings: • Exercise 9.4 All

  12. Angle Reasoning

  13. Exercises • Lines, Points and Triangles: • Exercise 9.5 All • Exercise 9.6 All • Exercise 9.7 All • Remember to give the right reason for your answer! • i.e x = 700: supplementary angles add to 1800

  14. A B I J F E Parallel Lines

  15. Exercises • Parallel Lines: • Exercise 9.8 All • Parallel Lines Solving for x • Exercise 9.9 All • Remember to give the right reason for your answer! • i.e x = 700: Alternate angles on parallel lines are equal

  16. Parts of a circle

  17. Exercise • Parts of a circle: • Exercise 10.1 All

  18. Angle Properties of Circles

  19. Exercise • Properties of a circle: • Exercise 10.2 All • Exercise 10.3 All • Exercise 10.4 All • Remember to give the right reason for your answer! • i.e x = 250: The angle at the centre is twice the angle at the circumference

  20. Rotational Symmetry • A figure has rotational symmetry about a point if it can rotate onto itself in less then 3600. • If a shape only rotates onto itself once then it is said to not have rotational symmetry • Order of Rotational Symmetry • The order of rotational symmetry is how often a shape will rotate onto itself • Every shape will have a rotational symmetry of at least 1

  21. Line Symmetry • A shape has line symmetry if it reflects or folds onto itself. The line or fold is called an axis of symmetry • Use a ruler to help you work out how many axis of symmetry a shape has

  22. Total Order of Symmetry • The Total Order of Symmetry of a shape is: • The number of Axis of Symmetry plus • The Order of Rotational Symmetry

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