2. The Chinese University of Hong Kong The Chinese University of Hong Kong EDD 5161F Educational Communications and Technology Group 14

3. Mathematics Target Audience: F.4 Science Students Duration: 2lessons Topic: Basic Properties of Circles

4. Basic Properties of Circles Angles in the semi-circle Angles in the semi-circle Angles in the semi-circle Angles in the semi-circle Angles in the same segment Angles in the same segment Angles in the same segment Angles in the same segment Basic terms of a circle Basic terms of a circle Basic terms of a circle Basic terms of a circle Angles at centre and circumference

5. I.Basic Terms of a Circle A B CD E O Chord Radius Diameter Arc Segment

6. II. Angles at centre and circumference y = 2x Reference:  at centre = 2  at circumference y x

7. Proof: m n x y x = 2m y = 2n x + y = 2 (m+n)  at centre = 2 (  at circumference)

8. Illustrative example: x yO Find x and y  at centre twice  at circumference

9. Quiz: y A. B. C. D. E. O Q.1

10. O x A. B. C. D. E. Q.2

11. III.Angle in the semi-circle Reference:  in the semi-circle A B C O 

12. Proof: O AB C  at centre twice  at circumference

13. Illustrative example: z O x  in the semi-circle ( base  s, isos  )

14. IV.Angle in the segment x = y Reference:  in the same segment x y

15. Proof: O x z y z = 2x  at centre twice  at circumference z = 2y  at centre twice  at circumference x = y

16. Illustrative example: A B C D y  in the same segment  in the semi-circle  sum of  O

17. Quiz: y x Find x and y  in the same segment Q.1

18. x A. B. C. D. E. Q.2

19. Revision on the properties of circles y x A B C O x y  in the same segment  in the semi-circle  at centre = 2  at circumference

20. THE END THE END

21. Prepared by Name Student No. Chan Chi Man Benjamin98040300 Wong Kwong Leung98118940 Chan Mei Ling97043700