GeoGebra Classroom

# Two distinct straight lines cannot intersect at more than one point

We can clearly see three lines. Two are red and one is green. We can change the positions of these three lines with free points A, B, C, D and E. We can see that the green line intersects the two red straight lines and makes interior angles α, β, У and δ. We can see that the interior angles on the right hand side of the green line are α and У (shown in blue color) and those on its left hand side are β and δ (shown in black color). P is the point of intersection of the two red lines. We have to find on which side of the green line will point P lie and what is the relation between this observation and the sum of the same side interior angles that the green line makes when it intersects the two red lines. Let us move the free points A, B, C, D and E and observe how the positions of the lines and the point P get changed.
Questions to think about 1. How does the position of point P change as we alter the angles α, β, У and δ. Also find α+ У and β+ δ. 2. Is it possible to have point P on the right hand side of the green line when α+ У>180˚?