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.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning