Conclusions of solid geometry

1. Two points in space determine a straight line, and three non-linear points determine a plane.

2. The problem of space is the relationship between points, lines and surfaces, which will be discussed separately below.

3. Point-to-point relationship: distance

The distance between two points is equal to the length of the line segment connecting the two points. (In European space, strictly speaking)

4. Line-line relationships: parallel, perpendicular, out-of-plane, angle, distance

Parallel: two straight lines in space are parallel and equivalent When two straight lines are on the same plane and have no common points.

Vertical: Two straight lines in space are perpendicular to the angle = 90 degrees, or one straight line is in a vertical plane of another straight line, or there is a parallel line of one straight line, and another straight line. The straight line is vertical. Once it exists, there are countless such parallel lines.

Different planes: Two straight lines are not in the same plane, and straight lines on different planes must not be parallel.

Angle: Generally speaking, the angle between straight lines on different planes can be converted into an angle on the same plane through parallel movement.

5. Face-to-face relationship: parallel, intersecting

Parallel: two planes that do not intersect are parallel to each other

Intersection: two planes intersect, common** A point is a straight line. If two points are common points of two planes, then the straight line passing through them is also the common intersection line of the two planes.

Angle: Two planes intersect with a plane perpendicular to the intersection line. The angle formed on the vertical plane is the angle between the two planes. Both rays of the angle are perpendicular to the intersection line.

6. Point-line relationship, same plane geometry.

7. Point-surface relationship: outside the plane, on the plane.

The solution to this kind of problem generally assumes one and proves the coincidence.

8. Line-plane relationships: perpendicular, parallel, intersection, angle

Vertical: A straight line perpendicular to a plane is equivalent to a straight line being perpendicular to all straight lines on a plane, equivalent to a straight line Being perpendicular to two non-parallel straight lines on a plane is equivalent to all planes passing through the straight lines being perpendicular to the plane.

Parallel: A straight line is parallel to a plane, which is equivalent to the fact that there is no common point, and it is equivalent to the existence of a plane through which the straight line is parallel to the plane. Equivalent to the fact that every point on the straight line is the same distance from the plane.

Intersection and angle: Draw a perpendicular line through a point on the straight line to the plane, and the line between the vertical foot and the focal point is called the photography of the straight line on the plane. The angle between a straight line and photography is the angle between a straight line and a plane.