The nature, definition and determination of the perpendicular line

<> "Perpendicular line refers to a straight line perpendicular to the midpoint of a line segment, and its properties, definitions and judgments are as follows:1Nature:

1) The distance from any point on the perpendicular line to the two ends of the line segment is equal; (2) the perpendicular line divides the line segment into two equal parts; (3) The straight line where the center line is located is perpendicular to the line segment. 2.Definitions:

A perpendicular line of a line segment is a straight line that coincides with the midpoint of the segment and is perpendicular to the segment. 3.Judgment:

1) Midpoint method: The triangle formed by the midpoint of the line segment connecting the two ends of the line segment and the two ends of the line segment, and the straight line corresponding to the center line of the triangle is the middle perpendicular line. (2) Perpendicular method:

A straight line that is connected perpendicular to another end point from one end of a line segment is a perpendicular line. (3) Inversion method: the plane of the line segment is inverted, then the midpoint of the line segment is inverted to the infinity point, the line where the line segment is located is inverted to the circle through the infinity point, the arc corresponding to any point on the line segment is inverted to the circle with the vector opposite to the point as the radius, and the vertical line of the line segment becomes the straight line where the two points on the circle are located after the inversion.

Definition of the mid-perpendicular line; : A straight line that is perpendicular to a line segment and bisects the line segment is called the perpendicular line of the line segment.

2.Any point on the perpendicular bisector is equal at the same distance from both ends of the segment.

3.If the two graphs are symmetrical with respect to a line, then the axis of symmetry is the perpendicular bisector of the corresponding point line.

4.The points on the vertical bisector of the segment are equal to the distance between the two endpoints of the segment.

5. The perpendicular bisector of the three sides of the triangle intersects at one point, which is called the outer center, and the distance from this point to the three vertices is equal (at this time, the outer center is the center of the circle, the length from the outer center to the vertex is the radius, and the circle made is the outer center of the triangle.

Determination of the perpendicular line: A point that is equal to the distance between the two ends of a line segment, on the vertical bisector of the line segment.

The perpendicular bisector line, or "perpendicular line" for short, is a very important part of the majority of geometry in junior high school.

Definition of a perpendicular bisector: A straight line that passes through the midpoint of a line segment and is perpendicular to the midline is called the perpendicular bisector (perpendicular line) of the line segment.

Nature of the perpendicular bisector:

2.Any point on the perpendicular bisector is equal at the same distance from both ends of the segment.

3.The perpendicular bisector of the three sides of the triangle intersects at a point called the outer center, and the distance from this point to the three vertices is equal.

The inverse theorem of the perpendicular bisector: to a point where the two endpoints of a line segment are at equal distances, on the perpendicular bisector of that line segment.

Determination of the perpendicular bisector: (1) the midpoint C of the straight line through the line segment AB and (2) the straight line CD line segment AB must be satisfied at the same time

The basic properties of perpendiculars are:

1. At a point on or outside a straight line, there is only one and only one straight line perpendicular to the known straight line (in the same plane).

2. From the outer point of the line to the line segment connected by each point on the line, the vertical line segment is the shortest.

The nature of the perpendicular segment: Of all the segments that connect a point outside the line with the points on the line, the perpendicular segment is the shortest.

The distance from the point to the lineThe length of the perpendicular segment from the point outside the line to the line is called the distance from the point to the line. If a point is on a straight line l, then the distance from this point to the straight line l is zero.

If the angle between two straight lines is a right angle, then it is said that these two straight lines are perpendicular to each other, and one of the straight lines is called the perpendicular line of the other straight line, and their intersection is called the perpendicular foot.

Properties and determination methods of perpendicular bisector:

Vertical bisector properties:

2) Any point on the perpendicular bisector line is at an equal distance to both ends of the line segment.

3) Triangles.

The perpendicular bisector of the three sides intersects at a point, which is called the outer center.

And the distance from this point to the three vertices is equal.

Determination method: Use definition: Passing through the midpoint of a line segment, and the straight line perpendicular to this line segment is the perpendicular bisector of the line segment.

A point at an equal distance from the two endpoints of a line segment, on the vertical bisector of the segment (that is, the vertical bisector of the line segment.

It can be thought of as a set of points at equal distances to the ends of a line segment).

A perpendicular line is a straight line that passes through the midpoint of a line segment and is perpendicular to that line segment, called the perpendicular bisector (perpendicular line) of the line segment. The perpendicular bisector can be seen as a set of points with equal distances to the two endpoints of a line segment, and the tung imitation bisector is an axis of symmetry of the line segment.

2) Any point on the perpendicular bisector line is at an equal distance to both ends of the line segment.

3) The perpendicular bisector of the three sides of the triangle intersects at a point, which is called the outer center, and the distance from this point to the vertex next to the three letters is equal.

4) Determination of the perpendicular bisector: (1) the midpoint of the straight line crossing the line segment must be met at the same time; (2) Straight line segments.

1. Define by local fiber: the straight line that passes through the midpoint of a certain line segment and is perpendicular to this line segment is the perpendicular bisector of the line segment.

2. A point where the distance between the two ends of a line segment is equal, on the vertical bisector of the line segment. (i.e., the perpendicular bisector of a segment can be thought of as a collection of points at equal distances from both ends of the segment).

3. The line perpendicular to the middle divides a line segment from the middle into two equal line segments, and perpendicular to the segmented line segment (at a 90° angle).

The basic properties of perpendiculars are:

1) A point on or outside a straight line of the pure family, where there is only one and only one line perpendicular to the known straight line.

2) From the outer point of the straight line to the point of the width of the trouser on the straight line, the vertical line segment is the shortest.

Categories: Education Science.

Problem description: What is the definition, nature and determination of perpendicular lines?

Analysis: The basic properties of perpendicular cavity are:

1) Passing a point on or outside a straight line, where there is only one or more straight lines perpendicular to a known straight line.

2) The vertical segment is the shortest of the segments from the outer point of the line to the points connected to each point on the line.