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Help with Geometry

  1. Mar 5, 2005 #1
    Hey Guys! I am really stuck on this questions:

    The medians BD and CE in triangle ABC are produced to X and Y respectively so that BD=DX and CE=EY. Prove that X,A, and Y lie in a straight line.

    I tried this question, it made no sense to me...i drew the picture and i named the interesting point between BD and CE "F". Then i proved that Traingle BYF is congruent to triangle CXF (SAS)...and then i have noo clue wut to do..PLz Help!!

    Thank u!
    Tanya
     
  2. jcsd
  3. Mar 5, 2005 #2

    Andrew Mason

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    Look at AXD and BCD and at AYE and BCE. Show that AX is parallel to BC and AY is parallel to BC (look at corresponding angles). If you can show this, then since AX and AY are parallel to the same line and share a common point, XAY would have to be a straight line.

    You can also show that XAC = ACB and CBA = BAY. Since CAB is the third angle in triangle ABC, ACB + CBA + CAB = 180 = XAC + BAY + CAB. The last three angles sum to XAY which means that XAY is a straight line (180 degrees).

    AM
     
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