There are two different ways you can plot the intersection points. This method is inaccurate because it is unlikely that you will succeed in getting the mouse exactly on the intersection point. If you succeed in constructing a counter example, then you have proved the Euclidean Theorem about adjacent angles false in Hyperbolic Geometry. Hyperbolic Angles are formed by the intersection of Hyperbolic rays analogous to the formation of angles in Euclidean Geometry. The following is a list of theorems about intersecting lines in Euclidean Geometry.
Vertical angles are congruent.
A Triangle is a closed figure formed by three line segments. The following is a list of theorems about Triangles in Euclidean Geometry. The sum of the angles of a Triangle is 180 degrees. The longest side of a Triangle is opposite the greatest angle. All three altitudes of a Triangle intersect in a single point.