Question

Доказать, что плоскость и прямая, не лежащая в ней, параллельны,если они имеют общий перпендикуляр. С РИСУНКОМ

Answer 1

_________________b
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|c |d
__________________a

Дано: а, б, с
Док-ть: а параллельно b
Док-во:
Можно достроить до прямоугольника
АВСД - прямоугольник, следовательно b параллельно а

Answer 2

Пусть нам дан. плоскость альфа и прямая а произвольная
если прямая не принадлежащая плоскости параллельна какой нибудь прямой этой плоскости то она параллельна и самой плоскости 
а если мы имеем прямую  которая перпендик.(прямая с) и плоскости и прямой то проведя прямую на плоскости (прямая в) увидим что прямая с перпендикулярна и прямой в
и если прямая с перпендикулярна и прямой в и прямой а то плоскость альфа и прямая а параллельны

Answer 3

Proving that a Plane and a Line, Not Lying in It, Are Not Parallel if They Have a Common Perpendicular

To prove that a plane and a line, not lying in it, are not parallel if they have a common perpendicular, we can use the following reasoning:

1. Definition of Parallel Lines and Planes: - Parallel lines are lines in a plane that do not intersect, and parallel planes are planes that do not intersect. - If a line and a plane do not intersect, they are considered parallel.

2. Common Perpendicular: - If a line and a plane have a common perpendicular, it means that the perpendicular line intersects the plane at a right angle.

3. Proof by Contradiction: - Assume that the plane and the line are parallel, even though they have a common perpendicular. - If they are parallel, the line should not intersect the plane, but the existence of a common perpendicular implies that they do intersect.

4. Conclusion: - Therefore, the assumption that the plane and the line are parallel, despite having a common perpendicular, leads to a contradiction. - Hence, the plane and the line, not lying in it, are not parallel if they have a common perpendicular.

Diagram

I'm unable to provide a diagram directly, but you can visualize the scenario with the line intersecting the plane at a right angle, indicating that they are not parallel despite having a common perpendicular.

This conclusion aligns with the principles of geometry and the definition of parallel lines and planes.