K-5. Use the Klein model to show that in the hyperbolic plane there exists a pentagon...

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K-5. Use the Klein model to show that in the hyperbolic plane there exists a pentagon with five right angles and there exists a hexagon with six right angles. (Hint: Begin with two lines having a common perpen- dicular. Locate the poles of these two lines, then draw an appropriate line through each of the poles, etc.) Does there exist, for all n ≥ 5, an n-sided polygon with n right angles? K-5. Use the Klein model to show that in the hyperbolic plane there exists a pentagon with five right angles and there exists a hexagon with six right angles. (Hint: Begin with two lines having a common perpen- dicular. Locate the poles of these two lines, then draw an appropriate line through each of the poles, etc.) Does there exist, for all n ≥ 5, an n-sided polygon with n right angles?

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