How to indicate that a point lies on a line. vertex E and vertex F are adjacent. side EF and side FA are adjacent

Main geometric shapes on a plane there are a point and a straight line. Points are usually denoted in capital Latin letters:
A, B, C, D, ... .

Direct lines are indicated in lowercase Latin letters:
a, b, c, d
In Figure 3 you see point A and straight line a.
infinite. In the figure we depict only part of the line, but imagine it extended indefinitely in both directions.

Look at Figure 4. You see lines a, b and points A, B, C. Points A to C lie on line a. We can also say that points A and C belong to straight a or that line a passes through points A and C.

Point B lies on line b. It does not lie on line a. Point C lies on both line a and line b. Lines a and b intersect at point C. Point C is the point of intersection of lines a and b.
In Figure 5 you see how a straight line is drawn using a ruler, passing through two given points A and B.

We will call the following properties the main properties of belonging of points and lines on a plane:

I. Whatever the line, there are points that belong to this line and points that do not belong to it.

Through any two points you can draw a straight line, and only one.

A straight line can be denoted by two points lying on it. For example, straight line o in Figure 4 can be designated AC, and straight line b can be designated BC.

Problem (3)". Can two lines have two points of intersection? Explain the answer.

Solution. If two lines had two points of intersection, then two lines would pass through these points. But this is impossible, since only one straight line can be drawn through two points. This means that two straight lines cannot have two points of intersection.

A. V. Pogorelov, Geometry for grades 7-11, Textbook for educational institutions