SPACE SUMMARY

MEET FIGURES IN SPACE

Line ┴ to a plane

  • If a line is perpendicular to 2 intersecting lines in a plane then it is perpendicular to the plane

Plane ┴ to a plane

If a line is perpendicular to a plane then every plane passing through this line is perpendicular to the plane

Line parallel to a plane:

If a line is parallel to 2 lines in the plane then it is parallel to the plane

Plane parallel to a plane:

If 2 intersecting lines in a plane are parallel to another 2 intersecting lines in another plane then the planes are parallel

Angle btw line and plane

how to prove :
The angle between a line, r, and a plane, π, is the angle between r and its orthogonal projection onto π, r'.

Dihedral angle

-we find the line of intersection

-we select a straight line from each plane perpendicular to the line of intersection

-the dihedral will be the angle between the 2 lines

Mediator plane:

how to prove :
method 1: prove that 3 pts are ebuidistant to the extrimities
method 2: The plane through the midpoint of a line segment and perpendicular to that segment, is called a mediating plane

Axis

how to prove that a line is an axis of the circle circumscribed about a triangle :
the line should be perpendicular to the plane on the vertex of the right triangle