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)
C
D
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
S right angles, and DAS  BAS
A B

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

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

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

31. e.g. (1985)
D C
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
S right angles, and DAS  BAS
A B
(i) Prove DA = AB
DAS  BAS given  A
AS is common S 
DSA  BSA  90 given  A

32. e.g. (1985)
D C
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
S right angles, and DAS  BAS
A B
(i) Prove DA = AB
DAS  BAS given  A
AS is common S 
DSA  BSA  90 given  A
 DAS  BAS  AAS 

33. e.g. (1985)
D C
In the diagram ABCD is a quadrilateral.
The diagonals AC and BD intersect at
S right angles, and DAS  BAS
A B
(i) Prove DA = AB
DAS  BAS given  A
AS is common S 
DSA  BSA  90 given  A
 DAS  BAS  AAS 
 DA  AB  matching sides in  's 

34. (ii) Prove DC = CB

35. (ii) Prove DC = CB
DA  AB proven S 

36. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A

37. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 

38. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 
 DAC  BAC SAS 

39. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 
 DAC  BAC SAS 
 DC  CB  matching sides in  's 

40. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 
 DAC  BAC SAS 
 DC  CB  matching sides in  's 
Types Of Triangles
Isosceles Triangle
A
B C

41. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 
 DAC  BAC SAS 
 DC  CB  matching sides in  's 
Types Of Triangles
Isosceles Triangle
A
AB  AC  sides in isoscelesABC 
B C

42. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 
 DAC  BAC SAS 
 DC  CB  matching sides in  's 
Types Of Triangles
Isosceles Triangle
A
AB  AC  sides in isoscelesABC 
B  C  ' s in isoscelesABC 
B C

43. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 
 DAC  BAC SAS 
 DC  CB  matching sides in  's 
Types Of Triangles
Isosceles Triangle
A
AB  AC  sides in isoscelesABC 
B  C  ' s in isoscelesABC 
B C
Equilateral Triangle
A
B C

44. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 
 DAC  BAC SAS 
 DC  CB  matching sides in  's 
Types Of Triangles
Isosceles Triangle
A
AB  AC  sides in isoscelesABC 
B  C  ' s in isoscelesABC 
B C
Equilateral Triangle
A AB  AC  BC sides in equilateralABC 
B C

45. (ii) Prove DC = CB
DA  AB proven S 
DAS  BAS given  A
AC is common S 
 DAC  BAC SAS 
 DC  CB  matching sides in  's 
Types Of Triangles
Isosceles Triangle
A
AB  AC  sides in isoscelesABC 
B  C  ' s in isoscelesABC 
B C
Equilateral Triangle
A AB  AC  BC sides in equilateralABC 
A  B  C  60 ' s in equilateralABC 
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