11 x1 t07 03 congruent triangles (2012)
TRANSCRIPT
![Page 1: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/1.jpg)
Congruent Triangles
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Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.
![Page 3: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/3.jpg)
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.
![Page 4: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/4.jpg)
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
![Page 5: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/5.jpg)
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)
![Page 6: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/6.jpg)
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)
![Page 7: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/7.jpg)
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)
![Page 8: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/8.jpg)
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)
![Page 9: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/9.jpg)
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)
![Page 10: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/10.jpg)
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)
![Page 11: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/11.jpg)
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)
![Page 12: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/12.jpg)
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)
![Page 13: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/13.jpg)
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)
![Page 14: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/14.jpg)
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)
![Page 15: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/15.jpg)
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
![Page 16: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/16.jpg)
(3) Angle-Angle-Side (AAS)
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(3) Angle-Angle-Side (AAS)
![Page 18: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/18.jpg)
(3) Angle-Angle-Side (AAS)
![Page 19: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/19.jpg)
(3) Angle-Angle-Side (AAS)
![Page 20: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/20.jpg)
(3) Angle-Angle-Side (AAS)
![Page 21: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/21.jpg)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position
![Page 22: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/22.jpg)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position(4) Right Angle-Hypotenuse-Side (RHS)
![Page 23: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/23.jpg)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position(4) Right Angle-Hypotenuse-Side (RHS)
![Page 24: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/24.jpg)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position(4) Right Angle-Hypotenuse-Side (RHS)
![Page 25: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/25.jpg)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position(4) Right Angle-Hypotenuse-Side (RHS)
![Page 26: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/26.jpg)
(3) Angle-Angle-Side (AAS)
NOTE:sides must be in
the same position(4) Right Angle-Hypotenuse-Side (RHS)
![Page 27: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/27.jpg)
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
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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
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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
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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
![Page 31: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/31.jpg)
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
![Page 32: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/32.jpg)
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
![Page 33: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/33.jpg)
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
![Page 34: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/34.jpg)
(ii) Prove DC = CB
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(ii) Prove DC = CB SABDA proven
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(ii) Prove DC = CB SABDA proven ABASDAS given
![Page 37: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/37.jpg)
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
![Page 38: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/38.jpg)
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC
![Page 39: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/39.jpg)
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
![Page 40: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/40.jpg)
(ii) Prove DC = CB SABDA proven
SAC common is ABASDAS given
SASBACDAC matching sides in 'sDC CB
Types Of TrianglesIsosceles Triangle
A
B C
![Page 41: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/41.jpg)
(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
![Page 42: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/42.jpg)
(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'
![Page 43: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/43.jpg)
(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
![Page 44: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/44.jpg)
(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
![Page 45: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/45.jpg)
(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
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Triangle Terminology
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Triangle Terminology
Altitude: (perpendicular height)Perpendicular from one side passing through the vertex
![Page 48: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/48.jpg)
Triangle Terminology
Altitude: (perpendicular height)Perpendicular from one side passing through the vertex
![Page 49: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/49.jpg)
Triangle Terminology
Altitude: (perpendicular height)Perpendicular from one side passing through the vertex
Median: Line joining vertex to the midpoint of the opposite side
![Page 50: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/50.jpg)
Triangle Terminology
Altitude: (perpendicular height)Perpendicular from one side passing through the vertex
Median: Line joining vertex to the midpoint of the opposite side
![Page 51: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/51.jpg)
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
![Page 52: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/52.jpg)
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
![Page 53: 11 x1 t07 03 congruent triangles (2012)](https://reader033.vdocuments.us/reader033/viewer/2022051017/55c07916bb61eb76438b45f6/html5/thumbnails/53.jpg)
Exercise 8C; 2, 4beh, 5, 7, 11a, 16, 18, 19a, 21, 22, 26