(A) Concurrent lines passthrough a given point.

If three or more lines pass through the same point then they are called concurrent lines and the common point is called the point of concurrency or concurrent point.

(B) Two distinct lines in a plane cannot have more than one point in common.

Let us suppose that the two lines intersect at two distinct points P and Q. But this assumption clashes with the axiom that only one line can pass through two distinct points. So, the assumption that we started with, that two lines can pass through two distinct points is wrong.

(C) Two distinct points in a plane determine a unique line.

For any two distinct points in space there is a unique line that passes through both of them.

(D) A line segment has two end points

A line segment has definite length. Its length can be measured. A line segment AB has two end points A and B. It starts from point A and ends at point B. One and only one line-segment can be between two given points A and B.