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Anonymous users2024-02-10A 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 intersection of the bisector of the three corners of a triangle is called the heart of the triangle. The inner part of the triangle is equal to the distance from the three sides, which is the center of the inscribed circle of the triangle.
The two angles bisector of the angle are equal and equal to half of the angle. The distance from the point on the angle bisector to both sides of the angle is equal.
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Anonymous users2024-02-09Angle bisector definition: A ray from the vertex of an angle, if the angle is divided into two equal angles, this ray is called the angle bisector.
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Anonymous users2024-02-08An angle bisector is a collection of points that are equally distant from both sides of the corner.
The distance from any point on the bisector of the angle (motion display) to both sides of the angle is equal.
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Anonymous users2024-02-07A 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.
Nature of the angular bisector:
1.The points on the bisector of the angle are equally distance to both sides of the angle.
2.The two angles bisector of the angle are equal and equal to half of the angle.
3.The three angular bisectors of a triangle intersect at a point and are at equal distances to each side, and this point is called the heart.
That is, with this point as the center of the circle, you can draw an inscribed circle inside the triangle.
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Anonymous users2024-02-06The ray that bisects an angle from the vertex of an angle is called the angular bisector of that angle.
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Anonymous users2024-02-05Angular bisector. Is a ray not a straight line, nor a line segment;
2) When an angle has an angular bisector, several mathematical expressions can be generated. It can be written as:
Because OC is the angular bisector of AOB, so.
AOB=2 AOC=2Baoc, or AOC= BOC=1 2 AOB, conversely, if AOC= COB, OC is the angular bisector of AOB.
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Anonymous users2024-02-04Angular bisector. Definition: The ray that bisects an angle is called the bisector of the angle.
The nature of the angular bisector: 1. The distance between any one of the points on the angular bisector and the two sides of the horn is equal.
2. Points that are equally distanced to both sides of the angle are on the bisector of this angle.
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Anonymous users2024-02-03Definition: The precise and concise explanation of the essential characteristics of a thing or the connotation and extension of a concept; Or by listing the basic properties of an event or an object to describe or standardize the meaning of a word or a concept.
The definition of an angular bisector is to explain what an angular bisector is: a ray is drawn from the vertex of an angle, and the angle is divided into two exactly the same angle, and this ray is called the angular bisector of the angle.
Nature: The nature of something is the fact that it is determined by that thing. That is, the fact that is certain to be correct according to the definition.
1. The two angles divided by the angle bisector are equal, and they are both equal to half of the angle. (Definition) 2, the distance from the point on the bisector of the angle to both sides of the angle is equal.
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Anonymous users2024-02-02Definition of the angular bisector: a ray 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.
Quality. 1. The two angles divided by the bisector of the repentant angle are equal, and they are equal to half of the angle. (Ridge Roll Definition).
2. The distance from the point on the bisector of the angle to the two sides of the corner is equal.
Judgment
Points at equal distances from the inside of the angle to both sides of the angle are on the bisector of the angle.
Hence according to the axiom of straight lines.
Proof: It is known that PD OA is in D, PE OB is in E, and PD=PE, and it is verified that OC bisects AOB.
Proof: In RT OPD and RT OPE:
op=op，pd=pe。
rt△opd≌rt△ope（hl）。
OC divides AOB equally.
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Anonymous users2024-02-01An angular bisector is a type of line segment used in geometry that divides an angle into two equal parts. It is usually used to calculate the midpoint or center point of an angle and to determine the point on two bisectors when a point and angle are given.
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Anonymous users2024-01-31An angular bisector is a ray drawn from the vertex of an angle to divide the angle into two identical angles, and this ray is called the angular bisector of the angle. The intersection of the three corners of the triangle is called the inner tie of the triangle. The inner part of the triangle is equal to the distance from the three sides, which is the center of the inscribed circle of the triangle
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Anonymous users2024-01-301.Angle bisector theorem: An angle bisector divides an angle into two equal angles.
2.Nature of the angular bisector: The distance from the point on the angular bisector to both sides of the angle is equal. （pc=pd）
3.Outer angular properties of an angular bisector: In a triangle, the points on the angular bisector are equal to the two angles on the outside of the adjacent edge of the corner.
4.Bisector properties of the outer angles of an angle: The bisector of the outer corner of an angle is equal to the bisector of the inner corner of the angle. Cha Feng.
5.The circumscribed circle nature of the angle bisector: the angle bisector of an angle is also the tangent line on the circumscribed circle corresponding to the angle.
6.The nature of the inscribed circle of the angle bisector: the angle bisector that is not stared at by the corner shed is also the tangent of the inscribed circle corresponding to the angle.
Extension] 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 angular bisector line and each line segment in the chain and triangle.
The property theorem of the bisector of the inner and outer angles of the triangle: the two line segments obtained by the inner and outer bisectors of the inner and outer angles of the triangle are proportional to the two sides of the angle between the two sides of the triangle and the extension line.
These theorems of angle bisector have important applications in geometry, where they can be used to solve problems such as angles, distances, proportions, and to prove the properties of triangles.
There is an angular bisector theorem, which is rarely used, but can be used to solve Olympiad problems. >>>More
Do dp perpendicular ab, dq perpendicular ac, because it is a bisector, then dq is equal to dp, because there is a ninety degrees, and because de is equal to df, so the triangle edp congruent triangle feq. So the angle deb is equal to the angle dfa, so: aed= dfc
The intersection of the angular bisector is called the heart. >>>More
Ask EF to be handed over to P
Because an bisects bac, de ab, df ac has de=df >>>More
The distance from the center of the circumscribed circle of the triangle to the three sides is equal, and in the triangle, the distance from the straight line passing through one corner to the two sides of the angle is equal, then the angle line is the angle bisector of the angle, and the center of the circle and the three vertices are connected, then these three are the angle bisector, and they intersect at one point - the center of the circle.