Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.7 Beyond Euclidean Geometry - Exercise Set 10.7 - Page 677: 44

Answer

Doesn’t make sense.

Work Step by Step

In Euclidean geometry, a basic assumption states that if there is a given line and a point is taken which is not on that given line, only one line can be drawn parallel to the given line and passing through that particular point. This assumption is used to prove that the sum of all the angles of a triangle is 180°. On the other hand, non-Euclidean geometries such as hyperbolic geometry and elliptic geometry do not assume the same. Therefore, the non-Euclidean geometries cannot be used to prove that the sum of a triangle’s angles is 180°. In these geometries, the sum of all the angles of a triangle is either less than (in case of hyperbolic geometry) or more than 180° (in case of elliptic geometry). The given statement does not make sense.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.