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Dao Trong Luan Coordinator

25/12/2017 at 11:41
Answers
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Let the triangle ABC and M be a point lying on the BC edge. Via point A straight line xy parallel BC. Through point M straight line parallel to AB, AC intersect the line xy in D and E respectively.

a, Prove that AD = BM and \(\Delta EMD=\Delta CAB\)

b, Prove that three lines AM, BD, EC concurrent

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  • ...
    Kaya Renger Coordinator 25/12/2017 at 19:27

    a) Apply properties of certain segments , we have :

    AD // BM 

    AB // MD 

    => AD = BM 

    Similar , we have EA = MC

    => AD + EA = BM + MC

    => DE = BC (1)

    We can see : \(\angle EDM=\angle ABC\)  (Because ED // BM , AD // MB)

                         \(\angle DEM=\angle ACB\)  (Because ED // BM , EM // AC)

    => \(\Delta MED=\Delta ACB\left(e-a-e\right)\)

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  • ...
    Faded 22/01/2018 at 12:42

    a) Apply properties of certain segments , we have :

    AD // BM 

    AB // MD 

    => AD = BM 

    Similar , we have EA = MC

    => AD + EA = BM + MC

    => DE = BC (1)

    We can see : ∠EDM=∠ABC

      (Because ED // BM , AD // MB)

                         ∠DEM=∠ACB

      (Because ED // BM , EM // AC)

    => ΔMED=ΔACB(e−a−e)


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