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 - Concept and Vocabulary Check - Page 676: 4

Answer

In Euclidean geometry, a basic assumption states that a given line and a point not on the line, one and only one line may be drawn through the given point parallel to the given line.

Work Step by Step

To prove that the sum of all the 3 angles of a triangle is , Euclid assumed that if a line is given and a point taken, which is not on the line, there can only be one line that passes through that point and parallel to the given line. There can be infinitely many lines passing through a certain point but one and only one line parallel to a given line that passes through that point.
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