1. Congruent Triangles

2. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.

3. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.

4. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS

5. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)

6. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)

7. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)

8. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)

9. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)

10. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)
(2) Side-Angle-Side (SAS)

11. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)
(2) Side-Angle-Side (SAS)

12. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)
(2) Side-Angle-Side (SAS)

13. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)
(2) Side-Angle-Side (SAS)

14. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)
(2) Side-Angle-Side (SAS)

15. Congruent Triangles
In order to prove congruent triangles you require three pieces of
information.
Hint: Look for a side that is the same in both triangles first.
TESTS
(1) Side-Side-Side (SSS)
(2) Side-Angle-Side (SAS)
NOTE:
must be
included
angle

16. (3) Angle-Angle-Side (AAS)

17. (3) Angle-Angle-Side (AAS)

18. (3) Angle-Angle-Side (AAS)

19. (3) Angle-Angle-Side (AAS)

20. (3) Angle-Angle-Side (AAS)

21. (3) Angle-Angle-Side (AAS)
NOTE:
sides must be in
the same position

22. (3) Angle-Angle-Side (AAS)
NOTE:
sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)

23. (3) Angle-Angle-Side (AAS)
NOTE:
sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)

24. (3) Angle-Angle-Side (AAS)
NOTE:
sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)

25. (3) Angle-Angle-Side (AAS)
NOTE:
sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)

26. (3) Angle-Angle-Side (AAS)
NOTE:
sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)

27. e.g. (1985)
A B
C
D
S
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
right angles, and BASDAS 

28. e.g. (1985)
A B
C
D
S
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
right angles, and BASDAS 
(i) Prove DA = AB

29. e.g. (1985)
A B
C
D
S
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
right angles, and BASDAS 
(i) Prove DA = AB
  ABASDAS given

30. e.g. (1985)
A B
C
D
S
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
right angles, and BASDAS 
(i) Prove DA = AB
  ABASDAS given
 SAS commonis

31. e.g. (1985)
A B
CD
S
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
right angles, and BASDAS 
(i) Prove DA = AB
  ABASDAS given
 SAS commonis
  ABSADSA given90


32. e.g. (1985)
A B
CD
S
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
right angles, and BASDAS 
(i) Prove DA = AB
  ABASDAS given
 SAS commonis
  ABSADSA given90

 AASBASDAS 

33. e.g. (1985)
A B
CD
S
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
right angles, and BASDAS 
(i) Prove DA = AB
  ABASDAS given
 SAS commonis
  ABSADSA given90

 AASBASDAS 
 matching sides in 'sDA AB   

34. (ii) Prove DC = CB

35. (ii) Prove DC = CB
  SABDA proven

36. (ii) Prove DC = CB
  SABDA proven
  ABASDAS given

37. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given

38. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given
 SASBACDAC 

39. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given
 SASBACDAC 
 matching sides in 'sDC CB   

40. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given
 SASBACDAC 
 matching sides in 'sDC CB   
Types Of Triangles
Isosceles Triangle
A
B C

41. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given
 SASBACDAC 
 matching sides in 'sDC CB   
Types Of Triangles
Isosceles Triangle
A
B C
 ABCACAB  isoscelesinsides

42. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given
 SASBACDAC 
 matching sides in 'sDC CB   
Types Of Triangles
Isosceles Triangle
A
B C
 ABCACAB  isoscelesinsides
 ABCCB  isoscelesins'

43. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given
 SASBACDAC 
 matching sides in 'sDC CB   
Types Of Triangles
Isosceles Triangle
A
B C
 ABCACAB  isoscelesinsides
 ABCCB  isoscelesins'
Equilateral Triangle
A
B C

44. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given
 SASBACDAC 
 matching sides in 'sDC CB   
Types Of Triangles
Isosceles Triangle
A
B C
 ABCACAB  isoscelesinsides
 ABCCB  isoscelesins'
Equilateral Triangle
 ABCBCACAB  lequilaterainsidesA
B C

45. (ii) Prove DC = CB
  SABDA proven
 SAC commonis
  ABASDAS given
 SASBACDAC 
 matching sides in 'sDC CB   
Types Of Triangles
Isosceles Triangle
A
B C
 ABCACAB  isoscelesinsides
 ABCCB  isoscelesins'
Equilateral Triangle
 ABCBCACAB  lequilaterainsides
 ABCCBA  lequilaterains'60
A
B C

46. Triangle Terminology

47. Triangle Terminology
Altitude: (perpendicular height)
Perpendicular from one side passing
through the vertex

48. Triangle Terminology
Altitude: (perpendicular height)
Perpendicular from one side passing
through the vertex

49. Triangle Terminology
Altitude: (perpendicular height)
Perpendicular from one side passing
through the vertex
Median: Line joining vertex to the
midpoint of the opposite side

50. Triangle Terminology
Altitude: (perpendicular height)
Perpendicular from one side passing
through the vertex
Median: Line joining vertex to the
midpoint of the opposite side

51. Triangle Terminology
Altitude: (perpendicular height)
Perpendicular from one side passing
through the vertex
Median: Line joining vertex to the
midpoint of the opposite side
Right Bisector: Perpendicular drawn
from the midpoint of a side

52. Triangle Terminology
Altitude: (perpendicular height)
Perpendicular from one side passing
through the vertex
Median: Line joining vertex to the
midpoint of the opposite side
Right Bisector: Perpendicular drawn
from the midpoint of a side

53. Exercise 8C; 2, 4beh, 5, 7, 11a, 16, 18, 19a, 21, 22, 26