The document discusses congruent triangles and the different tests that can be used to prove triangles are congruent. It states that in order to prove triangles are congruent, three pieces of information are required. It then lists and describes the four main tests: (1) Side-Side-Side, (2) Side-Angle-Side, (3) Angle-Angle-Side, and (4) Right Angle-Hypotenuse-Side. It provides an example proof using these tests and also defines different types of triangles like isosceles and equilateral triangles. Finally, it discusses some triangle terminology like altitude and median.
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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
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
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 isoscelesABC
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 isoscelesABC
B C ' s in isoscelesABC
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 isoscelesABC
B C ' s in isoscelesABC
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 isoscelesABC
B C ' s in isoscelesABC
B C
Equilateral Triangle
A AB AC BC sides in equilateralABC
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 isoscelesABC
B C ' s in isoscelesABC
B C
Equilateral Triangle
A AB AC BC sides in equilateralABC
A B C 60 ' s in equilateralABC
B C
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