Parallel planes

author: Петя
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Българска версия:

   From axiom 7 follows that if two different planes have one common point  М, then they have a common line.

• Definition: If two planes haven't got a common point, then these planes are parallel.
  

• Theorem 1: If two intersected lines (which are from one plane) are parallel respectively on two intersected lines (which are from other plane), then these planes are parallel

• Consequence 1: Trough point М (which is not from a goven plane х₁) passes only one plane х which is parallel on х₁.

            In a plane х₁: we get two intersected lines а₁ and b₁ and the point of intersected is М₁. If:

• а passes trough М, then а||a₁

• b passes trough М, then b||b₁,

• plane х (which is definited by intersected lines: а and b) passes trough М and x || х₁.

• Theorem 2: The line of intersection on planes with two parallel planes -are parallel lines. 
  

• Consequence 2: Two parallel planes х and х₁ devisit two parallel lines а and b equal segments.
  

• Consequence 3: Each points from one plane are on equal distances from another plane, if these two planes are parallel.

• Definiton: Distance between two parallel planes is called the distance from a point in the one plane to the other plane.

• Theorem 3: If two planes are perpendicular on the same line, then these plane are parallel

• Theorem 4: If a line is perpendicular on one of two parallel planes, then this line is also perpendicular on the other plane.