Question

Show that the dual to axiom P3 is true. That is, in Projective geometry, show that there exist three non-concurrent lines, where we say that two lines are concurrent if they have a point in common. P3: There exist three non-collinear points.

Answer 1

To prove the dual to Axiom P3 in projective geometry, we can show that there exist three non-concurrent lines by connecting three non-collinear points.

Step-by-step explanation:

In projective geometry, the dual to Axiom P3 states that there exist three non-concurrent lines. To prove this, we can use Axiom P3, which states that there exist three non-collinear points.

1. Draw three non-collinear points A, B, and C on a plane.
2. Let's connect point A with point B, point B with point C, and point C with point A.
3. These three lines are non-concurrent since they do not have any point in common. Therefore, we have shown that the dual to Axiom P3 is true.