1. Triangle Theorems

2. Triangle Theorems
A
The angle sum of any triangle is 180
B
C

3. Triangle Theorems
A
The angle sum of any triangle is 180
B A  B  C  180 sum ABC  180  
C

4. Triangle Theorems
A
The angle sum of any triangle is 180
B A  B  C  180 sum ABC  180  
C
Proof:

5. D
Triangle Theorems
A
The angle sum of any triangle is 180
E
B A  B  C  180 sum ABC  180  
C
Proof:
Construct DE||BC passing through A

6. D
Triangle Theorems
A
The angle sum of any triangle is 180
E
B A  B  C  180 sum ABC  180  
C
Proof:
Construct DE||BC passing through A
DAB  ABC alternate ' s , DE || BC 

7. D
Triangle Theorems
A
The angle sum of any triangle is 180
E
B A  B  C  180 sum ABC  180  
C
Proof:
Construct DE||BC passing through A
DAB  ABC alternate ' s , DE || BC 
EAC  ACB alternate ' s , DE || BC 

8. D
Triangle Theorems
A
The angle sum of any triangle is 180
E
B A  B  C  180 sum ABC  180  
C
Proof:
Construct DE||BC passing through A
DAB  ABC alternate ' s , DE || BC 
EAC  ACB alternate ' s , DE || BC 
DAB  BAC  CAE  180 straight DAE  180  

9. D
Triangle Theorems
A
The angle sum of any triangle is 180
E
B A  B  C  180 sum ABC  180  
C
Proof:
Construct DE||BC passing through A
DAB  ABC alternate ' s , DE || BC 
EAC  ACB alternate ' s , DE || BC 
DAB  BAC  CAE  180 straight DAE  180  
 ABC  BAC  ACB  180

10. A
B
C
D

11. A
The exterior angle of any triangle is equal
to the sum of the two opposite interior
B angles
C
D

12. A
The exterior angle of any triangle is equal
to the sum of the two opposite interior
B angles
ACD  A  B exterior , CAB 
C
D

13. A
The exterior angle of any triangle is equal
to the sum of the two opposite interior
B angles
ACD  A  B exterior , CAB 
C
D
Proof:

14. A
The exterior angle of any triangle is equal
to the sum of the two opposite interior
B E angles
ACD  A  B exterior , CAB 
C
D
Proof:
Construct CE||BA

15. A
The exterior angle of any triangle is equal
to the sum of the two opposite interior
B E angles
ACD  A  B exterior , CAB 
C
D
Proof:
Construct CE||BA
ABC  ECD corresponding ' s , CE || BA

16. A
The exterior angle of any triangle is equal
to the sum of the two opposite interior
B E angles
ACD  A  B exterior , CAB 
C
D
Proof:
Construct CE||BA
ABC  ECD corresponding ' s , CE || BA
BAC  ACE alternate ' s , CE || BA

17. A
The exterior angle of any triangle is equal
to the sum of the two opposite interior
B E angles
ACD  A  B exterior , CAB 
C
D
Proof:
Construct CE||BA
ABC  ECD corresponding ' s , CE || BA
BAC  ACE alternate ' s , CE || BA
ACD  ACE  ECD common 

18. A
The exterior angle of any triangle is equal
to the sum of the two opposite interior
B E angles
ACD  A  B exterior , CAB 
C
D
Proof:
Construct CE||BA
ABC  ECD corresponding ' s , CE || BA
BAC  ACE alternate ' s , CE || BA
ACD  ACE  ECD common 
 ACD  ABC  BAC

19. A
Polygon Theorems
B
C
D

20. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
C
D

21. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360  
C
D

22. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360  
Proof:
C
D

23. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360  
Proof:
C
D

24. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360  
Proof: sum ABC  180
C
D

25. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D

26. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360

27. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
B
C
A
D
E

28. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
The angle sum of any pentagon is 540
B
C
A
D
E

29. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
The angle sum of any pentagon is 540
B
A  B  C  D  E  540 sum ABCDE  540  
C
A
D
E

30. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
The angle sum of any pentagon is 540
B
A  B  C  D  E  540 sum ABCDE  540  
C Proof:
A
D
E

31. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
The angle sum of any pentagon is 540
B
A  B  C  D  E  540 sum ABCDE  540  
C Proof:
A
D
E

32. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
The angle sum of any pentagon is 540
B
A  B  C  D  E  540 sum ABCDE  540  
C Proof:
A sum ABE  180
D
E

33. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
The angle sum of any pentagon is 540
B
A  B  C  D  E  540 sum ABCDE  540  
C Proof:
A sum ABE  180
sum BED  180
D
E

34. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
The angle sum of any pentagon is 540
B
A  B  C  D  E  540 sum ABCDE  540 
C Proof:
A sum ABE  180 (+)
sum BED  180
D sum BDC  180
E

35. A
Polygon Theorems
B The angle sum of any quadrilateral is 360
A  B  C  D  360 sum ABCD  360 
Proof: sum ABC  180 (+)
C sum ADC  180
D
sum ABCD  360
The angle sum of any pentagon is 540
B
A  B  C  D  E  540 sum ABCDE  540 
C Proof:
A sum ABE  180 (+)
sum BED  180
D sum BDC  180
E
sum ABCDE  540

36. The angle sum of any polygon is 180n-2  ,

where n is the number of sides

37. The angle sum of any polygon is 180n-2  ,

where n is the number of sides
a
e b
c
d

38. The angle sum of any polygon is 180n-2  ,

where n is the number of sides
a
e b
The exterior angle sum of
any polygon is 360
c
d

39. The angle sum of any polygon is 180n-2  ,

where n is the number of sides
a
e b
The exterior angle sum of
any polygon is 360
c
d
a  b  c  d  e  360 exterior sum  360  

40. The angle sum of any polygon is 180n-2  ,

where n is the number of sides
a
e b
The exterior angle sum of
any polygon is 360
c
d
a  b  c  d  e  360 exterior sum  360  
Exercise 8B; 1dg, 2c, 3dh, 5ace, 6ab (iii), 7b, 8bfh, 9ad, 10dh,
11ad, 12c, 16, 18, 20