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Converse of a Theorem

  • 10-06-2012 1:07pm
    #1
    Registered Users, Registered Users 2 Posts: 3,989 ✭✭✭


    Hey, can anyone help me out and tell me what you're supposed to write for this question? I missed quite some time in Maths due to sport and other subject requirements so i'm a bit behind and have a feeling this will be on the paper tomorrow! The question is;

    (a) Explain what is meant by the converse of a theorem

    (b) There are some geometric statements that are true, but have converses that are false. Give one such geometric statement and state the false converse

    Thanks guys, bit lost right now so any help would be greatly appreciated!


Comments

  • Registered Users Posts: 187 ✭✭An0n


    (a) Pretty much the reverse of what the theorem states.

    (b) Example: All squares are parrallelograms, but not all par. are squares.


  • Registered Users Posts: 62 ✭✭ehshup


    (a) converse - if a theorem states "if A, then B," the converse of a theorem states "if B, then A." For example, if a theorem states that Opposite angles in a cyclic quadrilateral add to 180 degrees, the converse would be If opposite angles in a quadrilateral add to 180 degrees, then it is a cyclic quadrilateral.
    (b) take this for example- Statement: Equilateral triangles are shapes which do have 3 angles. Converse: If a shape has three angles, it is an equilateral triangle.
    Clearly the converse is false


  • Registered Users, Registered Users 2 Posts: 2,249 ✭✭✭Bears and Vodka


    (b) In a square, all sides are at right angles to each other.
    The false converse: if all sides in a shape are at right angles to each other then it's a square. (It's false because it can be a rectangle too)


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