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  • 8/6/2019 42964033 Secondary Parts of a Triangle

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    Secondary Parts of aSecondary Parts of a

    TriangleTriangle

    Prepared by:Prepared by:

    Ms. Fattie S. GuerreroMs. Fattie S. Guerrero

    22ndnd Term, SY 2007Term, SY 2007 -- 20082008

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    Objectives:Objectives:

    recall the primary parts of a triangle

    define and identify the secondary

    parts of a triangle: angle bisectors,altitudes and medians

    draw the secondary parts of atriangle

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    Secondary Parts of aSecondary Parts of aTriangleTriangle

    Angle Bisector

    of a Triangle

    Median of aTriangle

    Altitude of aTriangle

    Part Definition a segment which bisects anangle and whose endpoints are a

    vertex of the triangle and a pointon the opposite side

    a segment whose endpoints area vertex of the triangle and themidpoint of the opposite side

    a segment from the vertex ofthe triangle perpendicular to theline containing the opposite side

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    A

    B

    C

    D

    F E

    Examples:Examples: Identify the altitude, medianIdentify the altitude, medianand angle bisector of the following:and angle bisector of the following:

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    Perpendicular BisectorPerpendicular Bisectorof a Side of a Triangleof a Side of a Triangle

    a line perpendicular to the side at itsmidpoint and it is equidistant to theendpoints of the given segment

    LM

    Examples:

    JJ

    OOSS

    EE

    RR OO

    LL

    EE

    MM

    JJ AA

    MM

    II

    EE

    EO

    AM

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    Identify the altitude, median and angleIdentify the altitude, median and anglebisector of the following:bisector of the following:

    OE

    OE

    3. 4.

    JJ OO SS

    EERR

    MM

    OO

    EELL

    GG

    Median -

    Angle Bisector -

    Altitude - OE

    Median Angle Bisector

    Altitude

    MG

    OL

    RE

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    recall and identify secondary parts ofa triangle

    differentiate one secondary part of atriangle from another

    name and define the centers of atriangle

    construct the centers of a triangle

    Objectives:Objectives:

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    A

    B

    C

    D

    F E

    Examples:Examples: Identify the altitude, medianIdentify the altitude, medianand angle bisector of the following:and angle bisector of the following:

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    These are threeor more lines that

    meet at onepoint.

    The point at

    which they meetis the point ofconcurrency

    Concurrent linesConcurrent lines

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    INCENTER

    the point of

    concurrency of thethree angle bisectorsof a triangle

    the center of the

    incircle, the circleinscribed in thetriangle

    Centers of a TriangleCenters of a Triangle

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    CENTROID

    the point of

    concurrency of thethree medians

    it also called thecenter of mass

    the centroid divideseach median in aratio of 2:1

    Centers of a TriangleCenters of a Triangle

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    ORTHOCENTER

    the point of

    concurrency of thethree altitudes of atriangle

    Centers of a TriangleCenters of a Triangle

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    CIRCUMCENTER

    the point ofconcurrency of thethree perpendicularbisectors of the sidesof a triangle

    the center of thecircumcircle, thecircle circumscribedabout the triangle

    Centers of a TriangleCenters of a Triangle

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    Centers of a TriangleCenters of a Triangle

    Centers Concurrentlines

    Acute Right Obtuse

    Circumcenter

    Incenter

    Centroid

    Orthocenter

    Perpendicularbisectors of the

    sides

    Angle bisectors

    Medians

    Altitudes

    inside

    inside

    inside

    inside

    Midpoint ofthe

    hypotenuse

    inside

    inside

    Vertex ofthe right

    angle

    outside

    inside

    inside

    outside

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    Proving:Proving:

    Given: AB is theperpendicular bisectorof CD

    Prove: AB is the angle

    bisector ofCAD

    C

    A

    DB

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    Proving:Proving:

    Given: AB is a medianof(CAD, ABC is aright angle

    Prove: AC $ AD

    C

    A

    DB


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