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Are there two triangles with equal angles and a pair of equal sides which are not congruent? If yes, please give an example.

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    $\begingroup$ You're looking at the ASA and AAS rules of the congruency test. onlinemathlearning.com/prove-triangles-congruent.html $\endgroup$
    – Yiyuan Lee
    Oct 20, 2014 at 13:13
  • $\begingroup$ Do you mean that each of the three angles is the same on both triangles plus there is one side that is equal in both? $\endgroup$
    – flawr
    Oct 20, 2014 at 13:13
  • $\begingroup$ Yes, but the equal angles may not belong to the side. So we cannot apply the rule for congruent triangles. $\endgroup$
    – chen h.
    Oct 20, 2014 at 13:16

2 Answers 2

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For congruent triangle to exist, they must both share: SSS, SAS, ASA, AAS and HL. There for, on any two triangle with the same angles and a pair of equal sides, the "AAS" rule comes into play, and says, no, you cannot. Correct me if I'm wrong, but this is what I think.

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  • $\begingroup$ I think you are not right because the angles that belong to the side which is equal in both may not be equal?! $\endgroup$
    – chen h.
    Oct 20, 2014 at 13:19
  • $\begingroup$ But you said "two triangles with equal angles", I'm not sure what you're trying to say here.. @chenh. $\endgroup$ Oct 20, 2014 at 13:21
  • $\begingroup$ I mean that if we have triangles ABC and MNP with angles <M=<A, <N=<B and <P=<C, the equal sides may be for example AB=NP. $\endgroup$
    – chen h.
    Oct 20, 2014 at 13:23
  • $\begingroup$ @chenh. Ok, but you assume all 3 angles to be equal. Then how do you say in your first comment that "the angles that belong... may not be equal". Are all 3 angles equal or not? $\endgroup$
    – Jimmy R.
    Oct 20, 2014 at 13:25
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    $\begingroup$ See this ceemrr.com/Geometry1/RightTriangleAltitudes/paste_image6.gif $\endgroup$
    – chen h.
    Oct 20, 2014 at 13:35
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Take a right triangle, draw the attitude from the right angle. You then have several pairs of examples.

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  • $\begingroup$ Oh, yes - three pairs!!! $\endgroup$
    – chen h.
    Oct 20, 2014 at 13:25

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