Question

Докажите,что если данная прямая параллельна прямой,по которой пересекаются две плоскости ,и не лежит в этих плоскостях ,то она параллельна этим плоскостям

Answer 1

Данная прямая не лежит в первой плоскости и параллельна прямой (пересечение плоскостей),  лежащей в этой плоскости, по признаку параллельности плоскости и прямой, прямая параллельна этой плоскости. Аналогично со второй плоскостью. Данная прямая параллельна обоим плоскостям.

Answer 2

Proof that a line parallel to the intersection of two planes and not lying in those planes is parallel to those planes

To prove that a line parallel to the intersection of two planes and not lying in those planes is parallel to those planes, we can use the following reasoning:

Let's assume we have two planes, Plane A and Plane B, and a line L that is parallel to the intersection of Plane A and Plane B but does not lie in either plane.

To prove that line L is parallel to Plane A and Plane B, we need to show that any line segment drawn from line L to Plane A or Plane B is parallel to the corresponding line segment drawn from the intersection of Plane A and Plane B to Plane A or Plane B.

We can use the following steps to prove this:

1. Assume that line L intersects Plane A at point P and Plane B at point Q. 2. Draw a line segment from point P to any point on Plane A and another line segment from point Q to the corresponding point on Plane B. 3. Since line L is parallel to the intersection of Plane A and Plane B, the line segments drawn from line L to Plane A and Plane B will be parallel to the corresponding line segments drawn from the intersection of Plane A and Plane B to Plane A and Plane B. 4. By the transitive property of parallel lines, the line segments drawn from line L to Plane A and Plane B will be parallel to Plane A and Plane B, respectively. 5. Since any line segment drawn from line L to Plane A or Plane B is parallel to the corresponding line segment drawn from the intersection of Plane A and Plane B to Plane A or Plane B, we can conclude that line L is parallel to Plane A and Plane B.

Therefore, we have proven that if a line is parallel to the intersection of two planes and does not lie in those planes, it is also parallel to those planes.