Mutual position on two lines

author: Петя
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Българска версия:

            If two lines in a space, lyes in the same plane, then these lines can be:

• intersected – if they have a common point;

• parallel – if they've not a common point.

If two lines in a space, don't lye in the same plane, then these lines are called crossed lines.

            Parallel lines

• Theorem 1: In space: trough a point (which doesn't lye on a given line) passes just one line which is parallel on the given line.

• Theorem 2: If two lines are parallel, then each plane which crosses the one line, crosses and the other line.

• Theorem 3: In space: if two lines are parallel on a third line, then the first lines are also parallel.

           Angle between two crossed lines

• Theorem: Let's а and b are two corossed lines, and О₁ and О₂ – two different points in a space. Angle between line а₁ and b₁ (which pass trough О₁  and these lines are respectively parallel on а and b) is equal on an angle between lines а₂ and b₂ which pass trough point О₂ and which are respectively parallel on а and b.

• Definition: The angle between two crossed lines is angle between two intersected lines which are respectively parallel on the given crossed lines.

           Characteristic: Let's a and b are crossed lines and lines p and q are such: p||a, q||b. Then angle between lines p and q, is equal on angle between a and b.

• Definition: In a space two lines are perpendicular if angle between them is right angle.