11 x1 t06 03 congruent triangles
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Congruent Triangles
Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.
Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.
Hint: Look for a side that is the same in both triangles first.
Congruent TrianglesIn 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
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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)
Congruent TrianglesIn 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
(3) Angle-Angle-Side (AAS)
(3) Angle-Angle-Side (AAS)
(3) Angle-Angle-Side (AAS)
(3) Angle-Angle-Side (AAS)
(3) Angle-Angle-Side (AAS)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position
(4) Right Angle-Hypotenuse-Side (RHS)
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
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
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
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 common is
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 common is ABSADSA given 90
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 common is ABSADSA given 90 AASBASDAS
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 common is ABSADSA given 90 AASBASDAS matching sides in 'sDA AB
(ii) Prove DC = CB
(ii) Prove DC = CB SABDA proven
(ii) Prove DC = CB SABDA proven ABASDAS given
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of Triangles
Isosceles TriangleA
B C
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of Triangles
Isosceles TriangleA
B C
ABCACAB isoscelesin sides
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of Triangles
Isosceles TriangleA
B C
ABCACAB isoscelesin sides
ABCCB isoscelesin s'
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of Triangles
Isosceles TriangleA
B C
ABCACAB isoscelesin sides
ABCCB isoscelesin s'
Equilateral TriangleA
B C
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of Triangles
Isosceles TriangleA
B C
ABCACAB isoscelesin sides
ABCCB isoscelesin s'
Equilateral Triangle ABCBCACAB lequilaterain sides A
B C
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of Triangles
Isosceles TriangleA
B C
ABCACAB isoscelesin sides
ABCCB isoscelesin s'
Equilateral Triangle ABCBCACAB lequilaterain sides
ABCCBA lequilaterain s' 60
A
B C
Triangle Terminology
Triangle Terminology
Altitude: (perpendicular height)Perpendicular from one side passing through the vertex
Triangle Terminology
Altitude: (perpendicular height)Perpendicular from one side passing through the vertex
Triangle Terminology
Altitude: (perpendicular height)Perpendicular from one side passing through the vertex
Median: Line joining vertex to the midpoint of the opposite side
Triangle Terminology
Altitude: (perpendicular height)Perpendicular from one side passing through the vertex
Median: Line joining vertex to the midpoint of the opposite side
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
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
Exercise 8C; 2, 4beh, 5, 7, 11a, 16, 18, 19a, 21, 22, 26
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