How to make a midline on one side of a triangle with a compass

1.Adjust the compass, make two arcs with the two ends of the side as the center of the circle (the radius must be greater than half of the side length), and intersect at one point a.

2.Change the opening angle of the compass and repeat the above steps with different radii to get another intersection point B.

3.Connecting the two intersection points AB to make a straight line, intersecting the edge at the point C, C is the midpoint of the edge, and connecting the vertices of the triangle between C and the edge is the midline of the edge.

Principle: A and b are both points with the same distance from the two ends of the edge, so they are both on the perpendicular bisector of the edge, and the intersection of the perpendicular bisector and the edge is the midpoint.

Use the compass to take the two ends of the side to be the middle line as the center of the circle, and the distance less than the length of the side as the radius, draw two arcs on each side of the edge, and there will be an intersection point on each side, and then, connect the intersection point with a line, this line will have an intersection point with the edge, that is, the midpoint of this edge, and connect the vertices of the opposite side.

Make a perpendicular bisector on one side, and the intersection with the line segment is the midpoint of one side.

Perpendicular bisector method: On the two vertices of the ** segment, arc with any length greater than half of the line segment, respectively, there are two intersection points on both sides of the ** segment, and connect these two intersection points to obtain the vertical bisector.

Take one end of the edge as the center of the circle. Draw an arc for the radius of the side length greater than 1 2. (up and down the line segment) and then take the other end point as the center of the circle.

Draw an arc with the same length as before. Intersection arc with 2 points. Connect 2 points.

The intersection of this line and the edge is the midpoint. Then connect with the opposite corner of the edge.

1. Middle line: triangle ABC, vertices A, B, C, on the AB line segment, with A and B as the round point, any length is the radius to draw a circle, the intersection of the two circles on both sides of the ** section, connect the two intersection points to draw a straight line and the intersection of the AB line segment is the middle line of the AB side of the triangle ABC, that is, the perpendicular line;

Take two endpoints on either side of the triangle as the center of the circle, and get 1 2 as the radius of the side greater than this one, and connect the two circles to get two focal points, intersect and connect the point on that side of the triangle, and connect the midpoint of the triangle to get the middle line of that side.

Make the midpoint, connecting the vertices that the edge is on.

It should not be possible to do only the compass, and there must be a ruler.

Use a ruler to make the middle line of a triangle as follows:

1. Draw a triangle (black line) first.

2. Take the three vertices of the triangle as the center of the circle, and draw a circle (red line) with a radius greater than half of the corresponding side length of the two centers.

3. As shown in the figure below, erase the excess line segments (red lines) of the upper circle and retain the mating point of the infiltrated potato.

The three green lines are the middle lines of the triangle (it is generally necessary to keep traces of drawing dust).

Take the two vertices of the Sanqing angular shape as the center of the circle, and draw two arcs with the radius of more than half of the length of one side.

Two arcs intersect at two points, and the two intersections intersect on both sides of one of the sides, connecting the intersection, which is the perpendicular bisector of one of the sides of the triangle.

Properties: 2) Any point on the perpendicular bisector with equal distances 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 three vertices is equal.

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

Method: 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 line segment.

That is, the vertical bisector of the line segment can be seen as a set of points with equal distances to the ends of the line segment).

The center line of a triangle is the segment of a triangle that connects from the midpoint of an edge to a diagonal vertex. Therefore, a triangle can have 3 median lines.

The specific operation is as follows: Take the middle line of the AB side of the triangle ABC as an example.

1. Use the compass tool to keep the distance between the legs of the compass 2 3 of the length of ab. Then fix the fixed foot of the compass at point A, and draw a circle with the other foot at the fixed spacing as the radius.

2. After that, fix the fixed foot of the compass at point B, the spacing between the two feet remains the same, and the other foot draws a circle with the same spacing as the radius. At the same time, two arcs of the same size can be obtained and intersected to obtain two points e and f.

3. Use a ruler to connect the points E and F where two arcs intersect, and use two points to make a straight line and intersect the edge AB at the point D. The D point obtained here is actually the midpoint of AB.

4. According to the definition of the middle line of the triangle, use a ruler to connect AB diagonally C and D to draw a straight line, and the line segment AD obtained here is the middle line of the AB side of the triangle ABC.

Place one foot of the compass on the vertex, draw an arc with any line segment, and repeat the above steps at the intersection of the arc and the two edges, and then connect the first intersection.

In an isosceles triangle, the two ends of the bottom edge are the endpoints, and the radius is more than half the length of the bottom line, and the line between the intersection point of the two arcs and the vertex is the middle line.

The midpoint of the three sides can be found by using the three points as the center of the circle as the perpendicular bisector of the three sides.