4. We work in absolute geometry. (a) Suppose A, B and P are non-collinear and drop the per- pendicular from P to Q Є AB. If P lies between the perpendiculars l, m to AB through A and B, prove that Q is interior to AB. (Hint: show that the other cases are impossible) (b) Suppose there exists a triangle with angle sum 180°. Show A that there exists a right-triangle with angle sum 180° and P Q B therefore a rectangle. (Since rectangles are impossible in hyperbolic geometry, this proves part 2 of Theorem 4.19)

4. We work in absolute geometry. (a) Suppose A, B and P are non-collinear and drop the per- pendicular from P to Q Є AB. If P lies between the perpendiculars l, m to AB through A and B, prove that Q is interior to AB. (Hint: show that the other cases are impossible) (b) Suppose there exists a triangle with angle sum 180°. Show A that there exists a right-triangle with angle sum 180° and P Q B therefore a rectangle. (Since rectangles are impossible in hyperbolic geometry, this proves part 2 of Theorem 4.19)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 15E: Does the relation is complementary to for angles have a reflexive property consider one angle? A...

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