1 / 25

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.

trixie
Télécharger la présentation

Geometric Reasoning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related