Question

Can you prove the following assertions using only Euclid's postulates and common notions? Explain your answer....

Can you prove the following assertions using only Euclid's postulates and common notions? Explain your answer.

(a) Every line has at least two points lying on it

(b) For every line there is at least one point that does not lie on the line

(c) For every pair of points A not equal to B, there is only one line that passes through A and B.

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Answer #1

a) A straight line segment can be formed by joining any two points in space.

In Geometry, a line segment is a part of a line that is bounded by 2 distinct points on either end. It consists of a series of points bounded by the two endpoints. Thus a line segment is measurable as the distance between the two endpoints. A line segment is named after the two endpoints with an overbar on them.

c)Any straight line can be extended indefinitely on both sides. Unlike a line segment, a line is not bounded by any endpoint and so can be extended indefinitely in either direction. A line is uniquely defined as passing through two points which are used to name it.

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