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Math Help - [SOLVED] Congruency of lines?

  1. #1
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    [SOLVED] Congruency of lines?

    Hi, i;m really stuck on my maths homework.
    It's about congruency and stuff, but this is about proving that lines are the same?
    Anyhoo, here's the question:

    In the diagram, DX = XC, DV = ZC,and the lines AB and DC are parallel. Prove That:
    a) AX = BX
    b) AC = BD
    c) triangles DBZ and CAV are congruent

    my roughly drawn diagram to this question is here:
    http://i825.photobucket.com/albums/z...ers3/maths.jpg

    Please help i'm really stuck.

    If you need help reading the diagram just ask me what the matter is.

    Thankyou sooo much!!
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  2. #2
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    From the given we see that \Delta DXC is isosceles, so m\left( {\angle XDC} \right) = m\left( {\angle XCD} \right).
    By the use of alternate interiors angles we get m\left( {\angle CDB} \right) = m\left( {\angle DBA} \right)\;\& \,m\left( {\angle DCA} \right) = m\left( {\angle CAB} \right)
    From that we see that \Delta AXB is isosceles.

    Surely you can finish it from all the above.
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  3. #3
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    many thanks,

    could you help with this one aswell

    PQRS is a square and equilateral triangles PQA and RQB are drawn witgh A inside and B outside the square.

    By considering triangles PQR and AQB, prove that AB is equal to PR.

    Thankyouu
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  4. #4
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    Quote Originally Posted by doopers3 View Post
    could you help with this one aswell
    PQRS is a square and equilateral triangles PQA and RQB are drawn witgh A inside and B outside the square.
    By considering triangles PQR and AQB, prove that AB is equal to PR.
    If this is a new question, then by forum rules you must start a new thread.
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