(1) Given a straight line AB and a point C on the straight line, draw the perpendicular of the straight line AB;

(2) Given a straight line AB and a point C outside the straight line, draw the perpendicular of the straight line AB.

Drawing: make one right-angle side of a triangle coincide with a known straight line, move the triangle left and right along the straight line so that the other right-angle side passes through a known point, and draw a straight line along this right-angle side, then this straight line is the vertical line of the known straight line.

The nature of the vertical:

How many lines can you make by crossing a point P above (or outside) the known straight lines AB and AB as the vertical line of AB?

Through repeated practice and verification, we can get the first property: there is only one straight line perpendicular to the known straight line at one point.

As we know, a straight line is composed of countless points, any of which can be connected with a known point outside the straight line to form a line segment. Whether there is such a line segment, according to the first property, one and only one of these countless line segments is perpendicular to the known straight line, which is called a vertical line segment. Through measurement and demonstration, we can get the second property of verticality: among all the line segments connecting a point outside the straight line with a point on the straight line, the vertical line segment is the shortest. Simply put: the vertical line segment is the shortest.

To master the concepts of vertical line, vertical line segment and the distance from point to straight line; It is necessary to understand the special situation that the vertical line is the intersection line, contact the previous knowledge well, and draw the standard figure correctly with tools; The nature of the vertical line lays a foundation for future knowledge learning and should be mastered skillfully.