The theorem of the properties of the angle bisector line, the determination theorem of the angle bis

There is an angular bisector theorem, which is rarely used, but can be used to solve Olympiad problems.

Suppose the three edges are a, b, c

Then the length of the angle bisector of a = 1 (b+c)*b*c*(a+b+c)*(b+c-a).

Any point on the bisector of the angle is equal to the distance from both sides of the angle. Inverse theorem: Points that are equally distant to both sides of the angle are on the bisector of the angle.

There are three of them

Hehe, sorry

If we want to take our time slowly, we are waiting

It's a couple of pages, hehe, you go to the special ppt or lesson plan on the Internet, and it looks like it's there

The commonly used proof methods are area proof, vector proof...

Can you be specific?

The theorem for the bisector of an angle is that the distance from any point on the bisector of an angle to both sides of the angle is equal.

A ray is drawn from the vertex of an angle and the angle is divided into two identical angles, which is called the angle bisector of the angle. The determination theorem of the angle bisector: the distance from any point on the angle bisector to both sides of the angle is equal.

A ray (line within the corner) is drawn from the vertex of an angle and the angle is divided into two identical angles, which is called the angular bisector of the angle. The angle bisector is the trajectory of the angle within and on the shape to a point with equal distances on both sides of the angle.

There are two theorems for determining the bisector of angles.

Theorem 1: The distance from the point on the bisector of an angle to both sides of this angle is equal.

Theorem 2: The bisector of one corner of a triangle and the two segments formed by its opposite side are proportional to the correspondence of both sides of the angle. A ray is drawn from the vertex and the angle is divided into two identical angles, this line is called the angular bisector of the angle, and the property of the angular bisector is

The two angles bisector are equal, and the distance from the point on the bisector is equal to that of both sides of the angle.

The nature of the angular bisector is that the angular bisector can get two equal angles, and the distance from the point on the angular bisector to both sides of the angle is equal. This theorem has given mankind a good reference idea in architecture.

The proportional relationship of the angle bisector theorem is that the two line segments obtained by the opposite side of the angle bisector in the triangle are proportional to the two sides of the angle.

The line segment formed by the angular bisector of an angle (inner angle) of a triangle intersecting the points on the opposite side is called an angular bisector of the triangle. The theorem of the proportional relationship between line segments obtained by putting the angle bisector into the triangle can also be deduced from it and related formulas, and the quantitative relationship between the length of the angle bisector line in the triangle and each line segment can also be derived.

Area method. From the triangle area formula, obtained.

s abm = (1 2) ·ab·am·sin bams acm = (1 2)·ac·am·sin camam is the angular bisection of bac and the suture removed.

bam=∠cam

sin∠bam=sin∠cam

s△abm:s△acm=ab:ac

According to: contour bottom collinear, area ratio = base length ratio.

You can get: s abm:s acm=mb:mc, then ab:ac=mb:mc

Angle bisector high standby refers to the line segment that divides one angle into two equal angles.

The angle bisector divides the angle into two equal angles. In a triangle, if a line segment is bisector of an angle, the line segment divides the angle into two equal angles. Any point on the bisector of an angle is equal to the distance to both sides of the corner.

In a triangle, if a line segment is bisector of an angle, the line in which the segment is located divides the triangle into two triangles of equal area.

In a plane, if a straight line is bisector of two angles of two disjoint lines at the same time, then the line divides both angles into two equal angles at the same time. In a plane, if a straight line is bisector of the angles of two intersecting lines at the same time, then the line divides the two angles into four equal angles. In a quadrilateral, if a line segment is bisector of an angle, the line in which the segment is located divides the quadrilateral into two triangles of equal area.

Considerations for calculating angular bisectors

1. Definition of angle bisector: Angle bisector refers to a straight line that divides an angle into two angles of equal size, and the definition of angle bisector should be clarified.

2. The nature of the angle bisector: the angle bisector has some important properties, such as the intersection of the angle bisector at the apex of the angle, and the two small angles divided by the same size, etc., to be familiar with and master these properties.

3. Calculation method of angle bisector: The calculation of angle bisector can be calculated by using the angle bisector theorem, or it can be solved by geometric composition, and these calculation methods should be mastered.

4. Application of angular bisector: Angular bisector has a wide range of applications in solving geometric problems, such as the angular bisector theorem can be used to prove that two straight lines are parallel, and it is necessary to pay attention to the application method of angular bisector.

5. Pay attention to accuracy: When calculating the angular bisector, pay attention to accuracy, the higher the accuracy, the more accurate the calculation result.

Angular bisector linear manuscript crack theorem:

The distance from the point on the bisector of the angle to the two sides of the key is equal.

In AOB, OC bisects AOB, and the point P is on OC, and PE is OA on E, and PF is OB on F, then OE=OF. Dismantling.

The nature of the angular bisector: The angular bisector can get two equal angles, and the distance from the point on the angular bisector to both sides of the angle is equal.

1. The property of the angle bisector is mainly that the distance from the point on the bisector of the angle to both sides of the angle is equal.

2. The sex comic hypothem of the bisector of the inner angle of the triangle is that the inner angle bisector of the triangle becomes two line segments.

3. The bisector of one corner of the triangle intersects the opposite side of the angle.

The bisector of a triangle with an angle intersects the opposite side of the angle, and the line segment connecting the vertex of the corner with the intersection of the sock and the opposite side is called the angular bisector of the triangle (also called the inner bisector of the triangle).

By definition, the bisector of a triangle is a line segment. Since a triangle has three interior angles, a triangle has three angular bisectors. The intersection of the angular bisector of the triangle must be inside the triangle.

Angular bisector. How to draw the bisector of the angle: a

Take the apex of the corner as the center of the circle, draw an arc with the appropriate length as the radius, and intersect the two points with both sides of the angle; b.Draw an arc with two intersection points as the center of the circle, and the same length of 1 2 greater than the connecting segment of the two intersection points as the radius, and intersect at one point in the corner; c.The vertex of the passing angle and the intersection point in b are used as rays.

The ray is the bisector of the angle.

Angular bisector property theorem: The distance from the point on the angular bisector to both sides of the angle is equal. The inverse theorem of the property theorem: The point from the inside of the angle to the two sides of the angle at an equal distance is on the bisector of the angle in the horn.

The theorem of the properties of the angular bisector is that the distance from the point to both sides of the angle on the angular bisector is equal; The angle bisector determination theorem is that a point with equal distances to both sides of the angle is on the angle bisector; The angle bisector theorem selling impulse is the ratio theorem and the basis of Apollonius' circle theorem.

1. Angle bisector: The ray that divides an angle into two identical angles is called the bisector of the angle;

2. The theorem of the properties of the angle bisector: the distance from the point on the angle bisector to both sides of the angle is equal: the point on the bisector; the distance from the point to the edge;

3. The determination theorem of the angle bisector: the point with the equal distance to both sides of the angle is on the bisector of the land angle of the skin width.

In addition, please understand that your clever eyes are the driving force for my service.