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

1. The Angle Sum of a
Triangle

2. Prove that x + y + z = 180°
A
x
B
y
z
C

3. Construct PQ through A
so that PQ||BC
P
A
x
B
Q
y
z
C

4. ∠PAB = y°
(alternate angles, PQ||BC)
P
A
y x
B
Q
y
z
C

5. ∠QAC = z°
(alternate angles, PQ||BC)
P
A
y x
B
z
Q
y
z
C

6. Now PAQ is a straight line
P
A
y x
B
z
Q
y
z
C

7. x + y + z = 180°
(PAQ is a straight line)
P
A
y x
B
z
Q
y
z
C

8. x + y + z = 180°
A
x
B
y
z
C

9. The angle sum of a triangle is 180°
A
x
B
y
z
C

10. A different proof for the
same result

11. Prove that x + y + z = 180°
A
x
B
y
z
C

12. Produce BC to P
A
x
B
y
z
C
P

13. At C construct CQ||BA
A
x
B
Q
y
z
C
P

14. ∠ACQ = x°
(alternate angles, PQ||BC)
A
x
B
Q
y
z
x
C
P

15. ∠PCQ = y°
(corresponding angles, PQ||BC)
A
x
B
Q
y
z
x
C
y
P

16. Now BCP is a straight line
A
x
B
Q
y
z
x
C
y
P

17. x + y + z = 180°
(BCP is a straight line)
A
x
B
Q
y
z
x
C
y
P

18. x + y + z = 180°
A
x
B
y
z
C

19. The angle sum of a triangle is 180°
A
x
B
y
z
C