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GCSE Proof os square with equalaterial triangles

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  1. May 29, 2007 #1
    1. The problem statement, all variables and given/known data
    ABCD is a square and on side BC an equalaterial triangle is made extending to vertex E and another is made on line DC extending to vertex F. Prove that ECD is congruent to BCF.


    2. Relevant equations
    Proof is all about using algerbra to prove somthing right?
    If it's congruent it has to fit into 4 congruent rules:
    SSS
    ASA
    SAS
    RHS

    3. The attempt at a solution

    Well DC = BC

    but where now. I can descirbe it in words, but I believe u need to use albebra to prove it :(
     
  2. jcsd
  3. May 29, 2007 #2

    Kurdt

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    What are the properties of an equilateral triangle?
     
  4. May 29, 2007 #3
    3 even sides and 3 even anlges
     
  5. May 29, 2007 #4

    Kurdt

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    So you know at least two angles are the same and that one side is the same because they are sides of the same square.
     
  6. May 29, 2007 #5
    ASA, however the question is worth 3 marks. This question was in the mocks and I put:

    ED and BF are equal - i got the comment "how do you know"
    CF and CE are equal which gave me 1 mark out of 3
    SAS - this is wrong as it's ASA

    I dont see how I should get a "proper answer", I thought you have to use alegebra?
     
  7. May 29, 2007 #6

    Kurdt

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    The sides that you have stated are equal are sides that are not part of the original square. You must state specifically that the side of the triangles that is part of the square are equal and that is made under the assumption that the sides of a square are equal. The second assumption that you would take as self evident is that the angles in an equilateral triangle are all the same. These are reasonable in the GCSE framework.

    I don't know why you were given a mark for stating CF and CE are equal.

    Algebra is not always required in proofs. All you needed to do for this question was show that one of the conditions for congruence was satisfied using these geometrical arguments.
     
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