11x1 t08 03 congruent triangles (2011)
TRANSCRIPT
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 TrianglesIsosceles Triangle
A
B C
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of TrianglesIsosceles Triangle
A
B C
ABCACAB isoscelesin sides
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of TrianglesIsosceles Triangle
A
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 TrianglesIsosceles Triangle
A
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 TrianglesIsosceles Triangle
A
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 TrianglesIsosceles Triangle
A
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