1, definition: If the straight line L is perpendicular to the plane α, the straight line L is perpendicular to any straight line in the plane α.
2. Decision theorem: If a straight line in plane α is perpendicular to a vertical line of plane α, then this straight line is perpendicular to plane α.
3. Theorem of the perpendicularity of surfaces: If two planes are perpendicular, any straight line in one plane is perpendicular to the other plane.
4. Vector method: If the straight line L is perpendicular to any two vectors in the plane α, the straight line L is perpendicular to the plane α.
5. Projection method: If the projection of the straight line L on the plane α is 0, the straight line L is perpendicular to the plane α.
6. Reduction to absurdity: suppose that the straight line L is not perpendicular to the plane α, and there is a straight line M parallel to the plane α. At this time, the straight line L is parallel to or different from the straight line M, which contradicts what is known, so the assumption is not established, so the straight line L is perpendicular to the plane α.
7. Coordinate method: If the coordinate of a point in the spatial rectangular coordinate system is directly proportional to the coordinate of a point in another plane, then the point is on this plane, and it can be concluded that the line is perpendicular to the plane.
8. Triangle method: If the straight line L is perpendicular to the three sides of the triangle ABC, the straight line L is perpendicular to the plane ABC.
9. Projection method: If the projection of the straight line L on the plane α is 0, the straight line L is perpendicular to the plane α.
10, circle method: If the straight line L is tangent to the circle C, the straight line L is perpendicular to the plane α.
Knowledge expansion
Harmony is a basic concept in geometry and one of the basic elements of graphics.
A line is a geometric figure, which can be regarded as a collection of countless points. By definition, a line has no width or thickness, only length. In Euclidean geometry, a straight line is defined as the shortest distance between two points. The attributes of a straight line include length, direction and position. In analytic geometry, a straight line can be expressed by an equation, for example, y = kx+b.
A surface is a three-dimensional geometric figure, which can be regarded as a collection of countless points. By definition, a face has no height and width, only length and width. In Euclidean geometry, a plane is defined as a figure passing through a point and perpendicular to an infinite line parallel to the point.
The properties of a plane include length, width, direction and position. In analytic geometry, a plane can be represented by an equation, for example, z = kx+by+c.
Lines and surfaces are widely used in geometry. For example, in geometry, lines can be used to describe the outline and edge of an object, while faces can be used to describe the surface and shape of an object. In engineering, lines and curved surfaces can be used to design and manufacture objects with various shapes and structures, such as buildings, mechanical parts and electronic equipment.