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Is the following proof technically correct? I am aware that it might not seem typical, but me and my math teacher did not find why it isn't correct.

In a triangle ABC, given AB=AC, prove ∠B=∠C. (This is not a textbook problem, I created it out of my mind.)

In ∆ABC and ∆ACB:

AB=AC
∠A=∠A
AC=AB

∴ ∆ABC Is Congruent To ∆ACB

∴ ∠B=∠C

I am aware that there are alternatives. I can construct another triangle that is congruent to ∆ABC, in that order, and then prove it congruent to ∆ACB, in that order, but that adds complexity to my proof.

Number Basher
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  • So basically you are creating a similarity between the triangle and a reflected version of itself (using SAS postulate)? I think that works. The way you state it seems like you are just renaming the same triangle though. I might add primes to indicate the difference between the two triangles. Ex: A vs. A' – Kevin Jun 06 '22 at 08:24
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    This is Pappus' proof of the "Pons Asinorum" (aka, the Isosceles Triangle Theorem). ... BTW: If you want us to see your message to your instructor, please just enter the specific text of that message. Throwing a bunch of JSON on screen and requiring the reader to take it to another site to make any sense of it isn't helpful. – Blue Jun 06 '22 at 08:34
  • @KevinS I am in China and China assumes if you say two triangles are congruent angle A corresponds to angle D if you write ABC ~= DEF – Number Basher Jun 06 '22 at 08:49
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    Thank you @Blue and I think Blue is a good name... – Number Basher Jun 06 '22 at 08:53
  • "Mathematically correct" is a very long way of saying "correct"... – Mariano Suárez-Álvarez Oct 01 '22 at 06:52

1 Answers1

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The proof is mathematically correct.

aerile
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