Constructing the Perpendicular Line Through a Point on the Line

Consider the triangles and . The segments and are ______________  because ______________________ . Also segments and are ___________________  because ______________________ .  The segment is _______________ between the two given triangles.  Therefore the triangles and are _________________________ because ______________________________ .

Is the previous proof enough to say that line is perpendicular to line ? Explain your reasoning.

If a statement is false, correct it to make it true, or provide a counterexample.

1. Infinitely many perpendicular lines to a given line r pass through one of its points P.     
2. Given a line r and a point P belonging to the line, there always exists at least one line through P and perpendicular to r.        
3. If two intersecting lines form congruent vertical angles, then the two lines are mutually perpendicular.
4. Two perpendicular lines form 4 straight angles at their point of intersection.
5. The projection of a point onto the line it belongs to is the point itself.