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Determining Precisely Which Angles of a Triangle Are Congruent

  1. Sep 20, 2015 #1
    Hello,

    Suppose that I have two triangles ##\bigtriangleup ABC## and ##\bigtriangleup XYZ## that are known to be congruent by the side-side-side axiom, from which it follows that the parts are also congruent, such as the angles. My question is, how do I determine which of the three angles of ##\bigtriangleup ABC## is congruent to ∠ A, for example? Visually, it is clear that ##\angle A \cong X##, but I am having difficulty justifying this? Do I perform isometries until the vertices align, and then I can infer precisely which angles of ##\bigtriangleup ABC## are congruent to ##\bigtriangleup ABC##?

    congruent triangles.png
     
  2. jcsd
  3. Sep 20, 2015 #2

    micromass

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    I didn't know the side-side-side property was an axiom? It can definitely be proven! (Well, I suppose one could always make it an axiom, but I don't see the benefits in that).

    Anyway, if side a and side b are congruent to side a' and side b', then the angle between ab is congruent to the angle between a'b'. This should answer your question.
     
  4. Sep 21, 2015 #3

    HallsofIvy

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    Since you say you know that side BC, opposite to angle A is congruent to side YZ, opposite to angle X then it follows that angle A is congruent to angle X.
     
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