Hyperbolic triangles proof help?

[bonfire09]

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 I am 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 I am 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.

 

[SammyS]

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 I am 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 I am 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?

 

[bonfire09]

I've attached it.

 

[SammyS]

I've attached it.

OK I see it now.

I guess that it can take a while to appear initially.

 

[bonfire09]

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 I am also given that M and N are midpoints and I know somehow they allow me to do something but not quite sure.