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1.2 Using Segments and Congruence Notes - · PDF file · 2013-09-061.2 Using...

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1.2 Using Segments and Congruence Notes 1 1.2 Use Segments and Congruence Postulate/Axiom: A rule that is ACCEPTED WITHOUT proof Theorem: A rule that CAN BE proved using definitions, postulates, axioms, corollaries and other theorem. Ruler Postulate Points on a line can be matched one to one with the real numbers called coordinates. Always Positive. Distance between two points: #1 S U N #2 R A Y What is the difference in these two pictures? Segment Addition Postulate If B is between A and C, then AB + BC = AC segments with equal length. Congruent segments: The length of is equal to the length of is congruent to OR
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  • 1.2UsingSegmentsandCongruenceNotes

    1

    1.2UseSegmentsandCongruence

    Postulate/Axiom:ArulethatisACCEPTEDWITHOUTproof

    Theorem:ArulethatCANBEprovedusingdefinitions,postulates,axioms,corollariesandothertheorem.

    RulerPostulatePointsonalinecanbematchedonetoonewiththerealnumbers

    calledcoordinates.

    AlwaysPositive.Distancebetweentwopoints:

    #1

    SUN

    #2

    RAY

    Whatisthedifferenceinthesetwopictures? SegmentAdditionPostulate

    IfBisbetweenAandC,thenAB+BC=AC

    segmentswithequallength.Congruentsegments:

    Thelengthofisequaltothelengthof

    iscongruentto

    OR

  • 1.2UsingSegmentsandCongruenceNotes

    2

    Segmentadditionpostulate:BisbetweenAC.AB=2AC=7FindBC=

    BisbetweenACAC=23AB=x+1BC=3x2x=BC=

    x=6BC=16answer

    Ex2

    Midpoint:Pointwhichdividesasegmentinto2congruentparts.

    CisthemidpointofAB.AC=3x+5CB=2x+13x=AB=

    x=8AB=58

    Ex3

    answer

    BisthemidpointofAC.AB=4x1AC=10x20x=AB=

    x=9AB=35

    Ex4 cancreateatwocolumnproofasyousolve

    answer

    BisTHEMIDPOINTOFAC.AB=x+3CB=x+5AC=2x+2x=BC=

    Ex5

    x=18BC=23answer

    BoardworkSegmentAdditionandMidpointWorksheet.docx

    Youtryandwewillshareasajigsawinclass.

    1.OisbetweensegmentDG

    DO=3xOG=4x+1DG=36x=____OG=_____

    2.AisthemidpointofsegmentJC

    JA=5x+3AC=3x+11x=_____JC=_____

    3.OisthemidpointofsegmentBY

    BO=3x+16BY=14x4x=_____BY=______

    4.AisthemidpointofsegmentCT

    CA=x+2AT=3x+5CT=7x8x=____CT=____

  • Attachments

    SegmentAdditionandMidpointWorksheet.docx

    GeometryName: ____________________________

    Segment Addition & Midpoints

    1.

    is between and

    2.

    is the midpoint of

    3.

    is between and

    4.

    is the midpoint of

    5.

    is the midpoint of

    6.

    is between and

    7.

    is the midpoint of

    8.

    is between and

    9.

    is the midpoint of

    10.

    is the midpoint of

    D

    :

    29

    35

    Given

    LD

    EDx

    LEx

    =

    =

    =+

    :

    _____

    _____

    Find

    x

    LE

    =

    =

    ZP

    :

    217

    63

    Given

    EPx

    ZEx

    =+

    =-

    :

    _____

    _____

    _____

    Find

    x

    ZE

    ZP

    =

    =

    =

    L

    F

    Y

    :

    126

    15

    927

    Given

    FLx

    LY

    FYx

    =-

    =

    =+

    :

    _____

    _____

    _____

    Find

    x

    FL

    FY

    =

    =

    =

    R

    ES

    :

    87

    914

    Given

    ERx

    ESx

    =-

    =+

    :

    _____

    _____

    _____

    _____

    Find

    x

    ER

    RS

    ES

    =

    =

    =

    =

    A

    VL

    :

    35

    22

    711

    Given

    ALx

    VLx

    =+

    =-

    :

    _____

    _____

    _____

    Find

    x

    AL

    VA

    =

    =

    =

    E

    D

    H

    :

    2

    3

    3

    22

    5

    Given

    DEx

    DHx

    EHx

    =+

    =+

    =+

    :

    _____

    _____

    _____

    Find

    x

    DE

    DH

    =

    =

    =

    B

    AC

    :

    26

    3

    5

    4

    Given

    ACx

    BCx

    =+

    =+

    :

    _____

    _____

    _____

    Find

    x

    BC

    AC

    =

    =

    =

    C

    E

    B

    D

    :

    43

    813

    62

    Given

    BCx

    BDx

    CDx

    =+

    =+

    =+

    :

    _____

    _____

    _____

    _____

    Find

    x

    BC

    CD

    BD

    =

    =

    =

    =

    B

    AC

    :

    5

    6

    2

    912

    Given

    ABx

    ACx

    =+

    =-

    :

    _____

    _____

    _____

    Find

    x

    AC

    BC

    =

    =

    =

    C

    AB

    L

    :

    33

    51

    Given

    ACx

    CBx

    =+

    =-

    :

    _____

    _____

    _____

    Find

    x

    AC

    AB

    =

    =

    =

    SMART Notebook

    Page 1Page 2Attachments Page 1


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