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Can you prove similar triangles theorem by sine rule?

  • 10-06-2012 09:40PM
    #1
    finality
    Registered Users, Registered Users 2 Posts: 1,763 ✭✭✭


    Is it ok to prove the theorem "if 2 triangles are similar, their sides are proportional in order" by the sine rule? As in, let the angles in each equal a b and c, get sinb/sina for each triangle and then equate them and rearrange?

    It seems so simple... is it ok to prove it this way or am I doing something wrong?


Comments

  • #2
    leaveiton
    Closed Accounts Posts: 1,778 ✭✭✭leaveiton


    I don't know if they'd accept it that way. My teacher said something about having to prove them a certain way.


  • #3
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    finality wrote: »
    Is it ok to prove the theorem "if 2 triangles are similar, their sides are proportional in order" by the sine rule? As in, let the angles in each equal a b and c, get sinb/sina for each triangle and then equate them and rearrange?

    No. When you're asked to prove one of the theorems in geometry, you are only allowed to use the things that are listed before the thing you're proving. You're not allowed to use things that come after it.

    The whole idea of the sine of an angle is dependent on the similar triangles theorem. You can't use sines to prove a result when this result is needed in order to define sines in the first place. That's called "circular reasoning", and it's not logically valid. (Using A to prove B and then using B to prove A isn't kosher.)


  • #4
    finality
    Registered Users, Registered Users 2 Posts: 1,763 ✭✭✭finality


    MathsManiac wrote: »
    No. When you're asked to prove one of the theorems in geometry, you are only allowed to use the things that are listed before the thing you're proving. You're not allowed to use things that come after it.

    The whole idea of the sine of an angle is dependent on the similar triangles theorem. You can't use sines to prove a result when this result is needed in order to define sines in the first place. That's called "circular reasoning", and it's not logically valid. (Using A to prove B and then using B to prove A isn't kosher.)

    Thanks. :) I suspected it might be something like that.


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