Question

prove that every every line segment has one and only one end point . use euclids geometry to prove

Answer 1

it's false. A line segment is by definition finite in extent. So, it has two end points.

Since a line segment is non-directional, it makes no sense to call one end point a starting point.

A ray, on the other hand, has one end point, and extends indefinitely from it in a given direction.

Answer 2

Let us consider, a line segment AB.
Assume that it has two midpoints say C and D
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Recall that the midpoint of a line segment divides it into two equal parts
That is AC = BC and AD = DB
Since C is midpoint of AB, we have A, C and B are collinear
∴ AC + BC = AB → (1)
Similarly, we get AD + DB = AB → (2)
From (1) and (2), we get
AC + BC = AD + DB
2 AC = 2AD
∴ AC = AD
This is a contradiction unless C and D coincide.
Therefore our assumption that a line segment AB has two midpoints is incorrect.
Thus every line segment has one and only one midpoint.

Answer 3

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