Hyperbolic triangles proof help?

  • Thread starter bonfire09
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  • #1
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Homework Statement



Prove in hyperbolic geometry: In the accompanying figure M and N are the respective (hyperbolic) midpoints of AB and AC and θ and ∅ are the indicated angle measures. Determine, with proof, which of the following is true:
(1): θ=∅ (2): θ<∅ (3): θ>∅ ( stands for phi)


Homework Equations


I have attached a picture of the figure too. Since im in hyperbolic geometry I get to assume that the internal angle sum of a triangle <180 degrees and AAA congruence for triangles.


The Attempt at a Solution


I don't know where to get started. It looks simple but im thinking that I need to get congruent triangles in there somehow but I don't know how to. If you can give me a hint that be great.
 

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Answers and Replies

  • #2
SammyS
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Homework Statement



Prove in hyperbolic geometry: In the accompanying figure M and N are the respective (hyperbolic) midpoints of AB and AC and θ and ∅ are the indicated angle measures. Determine, with proof, which of the following is true:
(1): θ=∅ (2): θ<∅ (3): θ>∅


Homework Equations


I have attached a picture of the figure too. Since im in hyperbolic geometry I get to assume that the internal angle sum of a triangle <180 degrees and AAA congruence for triangles.


The Attempt at a Solution


I don't know where to get started. It looks simple but im thinking that I need to get congruent triangles in there somehow but I don't know how to. If you can give me a hint that be great.
Where's the figure?
 
  • #3
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I've attached it.
 
  • #4
SammyS
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I've attached it.
OK I see it now.

I guess that it can take a while to appear initially.
 
  • #5
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The only things that I can really with is triangle defect and the the internal angle sum of triangles are less than 180 degrees. In case of quad's they are less that 360. But im also given that M and N are midpoints and I know somehow they allow me to do something but not quite sure.
 

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