How to use the ruler as the midpoint of a line segment

Draw the midpoint of this line segment with a ruler:

1, line segment AB, as shown in the following figure:

2. Make a circle with A and B as the center and the length greater than 0.5AB as the radius, and intersect with C and D, as shown in the following figure:

3. Connect the CD, spanning AB and E, where E is the center of AB, as shown below:

4. Except auxiliary lines, point E is the center of line segment AB, as shown in the following figure:

Extended data:

Ruler painting means drawing only with rulers and compasses, not with scales.

Ruler drawing is a mathematical discipline that originated from ancient Greece. Only compasses and rulers are used, and only a limited number of times are allowed to solve different plane geometric drawing problems. Ruler The rulers and compasses used for drawing are imaginary and not exactly the same as those in reality:

1. The ruler must have no scale and be infinitely long, and can only be fixed on one side with the ruler. You can only use it to connect two points together, and you can't draw scales on them;

Compasses can be opened to infinite width, but there can't be scales on them. It can only be pulled out to the length of the previous structure.

In the stage of compulsory education, students' first contact with rulers is to "make a line segment equal to a known line segment".

The five prerequisites for drawing a ruler are:

1. Allows you to select any point within a certain range on a plane, a straight line or an arc (the so-called "certain range" is based on the following four rules).

2. The position order of different points on the same straight line can be judged.

3, can judge the position order of different points on the same arc.

You can judge which side of the straight line a point on the plane is on.

5. It can be judged whether a point on the plane is inside or outside the circle.

The five public laws drawn by ruler and ruler are:

1. Make a straight line through these two determined points.

2. Make a circle with a certain point as the center and the distance between two certain points as the radius.

3. Determine the intersection of two intersecting lines.

4. Determine the intersection of the intersection circle and the straight line.

5. Determine the intersection of two intersecting circles.

Baidu Encyclopedia-Ruler Drawing

A word with ten thousand radicals.