Solution: as shown in the figure: connecting MN,

Open a warehouse at the intersection point p between the bisector of the middle vertical line in MN and ∠AOB.

The reason is:

∫p is on the bisector of∝∠ ∝∠AOB,

∴p The distance to the two highways is equal,

P is on the perpendicular bisector of MN,

∴pM=pN，

P is what you want.

(1) Angle bisector exercise:

In the angle AOB, draw the bisector of the angle

Method 1:

1. Draw an arc with point O as the center and any length as the radius. The two sides of the intersection angle AOB of two arcs are at point M and point N respectively.

2. Draw an arc with points M and N as the center and the length greater than 1/2MN as the radius, and the two arcs intersect at point P. ..

3. Perform ray operation.

The ray OP is the bisector of the angle AOB.

Of course, there are many ways to do the angle bisector. Next, a ruler drawing method is provided for your reference.

Method 2:

1. Intercept OM, OA and ON, OB on both sides of OA and OB to make OM=ON and OA = OB.

2. Connect AN and BM, which intersect at point P;

3. Perform ray operation.

The ray OP is the bisector of the angle AOB.

Angular bisector:

The bisector of an angle of a triangle intersects the opposite side of the angle, and the line segment connecting the vertex of the angle and the opposite side is called the bisector of the triangle (also called the bisector of the inner angle of the triangle). By definition, the bisector of a triangle is a line segment. Because a triangle has three internal angles, it has three bisectors. The intersection of the bisectors of a triangle must be inside the triangle.

Angle line theorem;

The distance from any point on the bisector of (1) angle to both sides of the angle is equal. The shortest distance is perpendicular to both sides.

② The bisector of the angle can get the same two angles, both of which are equal to half of the angle.

③ The three bisectors of a triangle intersect at a point, and the distance from the point to the three sides is equal.

(4) The bisectors of the three angles of a triangle intersect at a point, which is called the center, that is, an inscribed circle can be drawn inside the triangle with this point as the center.

Inverse theorem:

Within an angle, points with equal distances to both sides of the angle are on the bisector of the angle.

Note: 20 12 Lanzhou senior high school entrance examination mathematics, there are two answers, that is, the outer foot has also made a bisector. This is the original title of the eighth grade math period 20 13-20 14 in Huludao city. As shown in the figure, there is only one answer, but if you think about it carefully, please make two (no reduction).

Thank you&; #9787;