Is it possible that two triangles satisfy these conditions?

Question

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

You're looking at the ASA and AAS rules of the congruency test. http://www.onlinemathlearning.com/prove-triangles-congruent.html — Yiyuan Lee, Oct 20 '14 at 13:13
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? — flawr, Oct 20 '14 at 13:13
Yes, but the equal angles may not belong to the side. So we cannot apply the rule for congruent triangles. — chen h., Oct 20 '14 at 13:16

score 0 · Answer 1 · answered Oct 20 '14 at 13:16

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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.

answered Oct 20 '14 at 13:16

Sam Chahine

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I think you are not right because the angles that belong to the side which is equal in both may not be equal?! – chen h. Oct 20 '14 at 13:19
But you said "two triangles with equal angles", I'm not sure what you're trying to say here.. @chenh. – Sam Chahine Oct 20 '14 at 13:21
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. – chen h. Oct 20 '14 at 13:23
@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? – Jimmy R. Oct 20 '14 at 13:25
I drew both triangles out, still don't see how it's possible? If you do figure it out please enlighten me! @chenh. – Sam Chahine Oct 20 '14 at 13:26
Yes, all three angles are equal. Someone already answered. There are such triangles. – chen h. Oct 20 '14 at 13:26
Can you add a diagram to your answer to help us further understand? @chenh. – Sam Chahine Oct 20 '14 at 13:28
I dont know how to do it. Just take a right triangle and draw the altitude. You have 3 pairs of such triangles. – chen h. Oct 20 '14 at 13:29
Still doesn't make sense, anyway, glad you found your answer.. @chenh. – Sam Chahine Oct 20 '14 at 13:31
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See this http://ceemrr.com/Geometry1/RightTriangleAltitudes/paste_image6.gif – chen h. Oct 20 '14 at 13:35
ahh I see, makes more sense now, thanks. @chenh. – Sam Chahine Oct 20 '14 at 13:39

score 0 · Answer 2 · answered Oct 20 '14 at 13:22

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Take a right triangle, draw the attitude from the right angle. You then have several pairs of examples.

answered Oct 20 '14 at 13:22

Quang Hoang

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Oh, yes - three pairs!!! – chen h. Oct 20 '14 at 13:25

Is it possible that two triangles satisfy these conditions?

2 Answers2