Prove that G divides AC into two equal segments, if CA is paralel to ED?

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  • Pope
    Lv 7
    2 years ago
    Favorite Answer

    This is going to be somewhat abbreviated. First prove these similarity statements:

    ∆EHF ~ ∆AGF

    ∆DHF ~ ∆CGF

    Therefore, CG/DH = AG/EH = GF/HF

    ∆BHE ~ ∆BGC

    ∆BHD ~ ∆BGA

    Therefore, CG/EH = AG/DH = BG/BH

    CG/DH = AG/EH and CG/EH = AG/DH

    (CG/DH)(CG/EH) = (AG/EH)(AG/DH)

    CG²/[(DH)(EH)] = AG²/[(DH)(EH)]

    CG² = AG²

    CG = AG

  • 2 years ago

    :

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