Geometry – 4

1. Angles • Use of Protractor • Types of Angles Geometry – 4 Tips and tools for creating and presenting wide format slides

2. Angles In Daily Life If we look around us, we will see angles everywhere.

3. A B C Ray BAand rayBCare called thearmsof ABC. What Is An Angle ? When two non-collinear rays join with a common endpoint (origin) an angle is formed. Ray BA B Common endpoint Ray BC Common endpoint is called the vertex of the angle.Bis thevertexof ÐABC. Ray BA and BC are two non-collinear rays

4. Fact: We can also think of an angle formed by rotating one ray away from its initial position.

5. A B C Naming An Angle To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. For example: ÐABC or ÐCBA We may also name this angle only by the single letter of the vertex, for example the above angle can be named using middle letter as ÐB.

6. A X R P F T B C Interior And Exterior Of An Angle An angle divides the points on the plane into three regions: • Points lying on the angle (An angle) • Points within the angle (Its interior portion.) • Points outside the angle (Its exterior portion.)

7. Measurement Of An Angle Protractor is used to measure and draw angles. Angles are accuratelymeasured in degrees.

8. Protractor is a Geometrical instrument used for measuring angle between two lines.

9. Inside scale from 0o to 180o going in an anti-clockwise direction. Outside scale from 0o to 180o going in a clockwise direction. A 180o Protractor

10. You need to be able to measure an angle to the nearest degree. To help you do this you should always: 1. Look directly down onto the cross point. (this avoids parallax errors) 2. Always use the protractor in a horizontal manner as shown below. 

11. 1 0 on the inside so use inside scale 2 0 on the outside so use outside scale Measuring Angles with a 180o Protractor 50o 67o

12. 3 4 0 on the inside so use inside scale 0 on the outside so use outside scale Measuring Angles with a 180o Protractor 120o 135o

13. Measure each angle in the shapes below. 900 2 3 1 670 670 680 900 900 1120 680 900 460 1120 6 5 4 480 1180 730 1070 900 1010 1010 420 1100 1100 1070 730 Rectangle 3600 Trapezium 3600 Triangle 1800 Parallelogram 3600 Triangle 1800 Pentagon 5400

14. B A A A B C B B C A C C Types Of Angles There are four main types of angles. Right angle Acute angle Obtuse angle Straight angle

15. Right angle: An angle whose measure is 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle

16. Examples Of Right Angle

17. Obtuse angle: An angle whose measure is greater than 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle

18. Examples Of Obtuse Angle

19. Acute angle: An angle whose measure is less than 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle

20. Examples Of Acute Angle

21. Straight angle: An angle whose measure is 180 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle

22. Examples Of Straight Angle

23. Estimate the Angles and name the type of angle you have measured 1 2 4 3 Test Yourself 27 degrees / Acute angle 75 degrees/Acute Angle 90 degrees / Right angle 30 degrees/Acute Angle

24. You measure and name the angles

25. Test Your Self 1 2

26. Measure each angle in the shapes below. 2 3 1 6 5 4