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Math Help - Congruent Segments

  1. #1
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    Congruent Segments

    Given segment NQ bisects angle MNP and angle M is congruent to angle P, prove segment MQ is congruent to segment PQ.
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  2. #2
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    Quote Originally Posted by magentarita View Post
    Given segment NQ bisects angle MNP and angle M is congruent to angle P, prove segment MQ is congruent to segment PQ.
    Hello,

    Given:

    \overline{NQ} bisects \angle MNP and \angle M \cong \angle P

    Reflexive Property of Congruence:

    \overline{NQ} \cong \overline {NQ}

    Definition of Angle Bisector

    \angle MNQ \cong \angle PNQ

    AAS: (Angle-Angle-Side Congruency Theorem)

    \triangle MNQ \cong \triangle PNQ

    CPCTC (Corresponding Parts of Congruent Trinagles are Congruent)

    \overline{MQ} \cong \overline{PQ}
    Attached Thumbnails Attached Thumbnails Congruent Segments-tri.bmp  
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  3. #3
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    ok....

    Quote Originally Posted by masters View Post
    Hello,

    Given:

    \overline{NQ} bisects \angle MNP and \angle M \cong \angle P

    Reflexive Property of Congruence:

    \overline{NQ} \cong \overline {NQ}

    Definition of Angle Bisector

    \angle MNQ \cong \angle PNQ

    AAS: (Angle-Angle-Side Congruency Theorem)

    \triangle MNQ \cong \triangle PNQ

    CPCTC (Corresponding Parts of Congruent Trinagles are Congruent)

    \overline{MQ} \cong \overline{PQ}
    Wonderfully done!
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