11x1 t08 03 congruent triangles (2011)

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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 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' 60A

    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

    Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number