The concept of median vertical line: The straight line passing through the midpoint of a line segment and perpendicular to this line segment is called the median vertical line of this line segment.
Properties of the perpendicular line: 1. Perpendicular bisector is vertical, bisect its line segment.
2. The distance from any point on the perpendicular bisector to both ends of the line segment is equal.
3. The perpendicular lines of the three sides of a triangle intersect at a point, which is called the outer center, and the distance from the point to the three vertices is equal.
Inverse theorem of median vertical line: the equidistant points of two endpoints of a line segment are on the median vertical line of this line segment.
As shown in the figure: the straight line MN is the middle vertical line of the line segment AB.
Note: To prove that a straight line is the middle perpendicular of a line segment, it is necessary to prove that the distance between two points and this line segment is equal and both points are on the straight line to be proved.
Generally speaking, perpendicular bisector will be used with congruent triangles.
The nature of the median vertical line: the point on the median vertical line of a line segment is equal to the distance between the two endpoints of the line segment.
Clever method: the distance from the point to both ends of the line segment is equal.
Congruent triangles can be used to prove it.
Ruler practice of middle vertical line:
Method 1:
1, take the midpoint of the line segment.
2. Draw an arc with the two endpoints of the line segment as the center and the radius greater than half the length of the line segment. Get an intersection point.
3. Connect these two intersections.
Principle: The height of an isosceles triangle bisects the base vertically.
Method 2:
1. Draw an arc with the two endpoints of the line segment as the center and the radius greater than half the length of the line segment as the radius to get two intersections. Principle: The radius of a circle is equal everywhere.
2. Connect these two intersections. Principle: two points are on a line.
The nature of isosceles triangle;
1, three lines one
2. Equiangular equilateral