Top Drawer Teachers: Two proofs of the angle sum of a triangle

1,661 views

Published on

Top Drawer Teachers
The Australian Association of Mathematics Teachers (AAMT) Inc.
http://topdrawer.aamt.edu.au

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,661
On SlideShare
0
From Embeds
0
Number of Embeds
902
Actions
Shares
0
Downloads
23
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Top Drawer Teachers: Two proofs of the angle sum of a triangle

  1. 1. The Angle Sum of a Triangle
  2. 2. Prove that x + y + z = 180° A x B y z C
  3. 3. Construct PQ through A so that PQ||BC P A x B Q y z C
  4. 4. ∠PAB = y° (alternate angles, PQ||BC) P A y x B Q y z C
  5. 5. ∠QAC = z° (alternate angles, PQ||BC) P A y x B z Q y z C
  6. 6. Now PAQ is a straight line P A y x B z Q y z C
  7. 7. x + y + z = 180° (PAQ is a straight line) P A y x B z Q y z C
  8. 8. x + y + z = 180° A x B y z C
  9. 9. The angle sum of a triangle is 180° A x B y z C
  10. 10. A different proof for the same result
  11. 11. Prove that x + y + z = 180° A x B y z C
  12. 12. Produce BC to P A x B y z C P
  13. 13. At C construct CQ||BA A x B Q y z C P
  14. 14. ∠ACQ = x° (alternate angles, PQ||BC) A x B Q y z x C P
  15. 15. ∠PCQ = y° (corresponding angles, PQ||BC) A x B Q y z x C y P
  16. 16. Now BCP is a straight line A x B Q y z x C y P
  17. 17. x + y + z = 180° (BCP is a straight line) A x B Q y z x C y P
  18. 18. x + y + z = 180° A x B y z C
  19. 19. The angle sum of a triangle is 180° A x B y z C

×