Точка м не лежит в плоскости прямоугольника ABCD. докажите что прямая CD параллельна плоскости ABM

To prove that line CD is parallel to plane ABM, we need to show that the line formed by any two points on CD lies entirely in the plane ABM.

Let's consider two arbitrary points on line CD, P and Q.

Since point M does not lie in the plane of rectangle ABCD, consider the plane that contains points P, Q, and M. Let's denote this plane as PQM.

Now, let's consider the line formed by connecting points A and B. Since ABCD is a rectangle, line AB is parallel to line CD.

Since both AB and CD are parallel to the same plane, PQM, this means that line CD is also parallel to plane ABM.

Therefore, we have successfully proven that line CD is parallel to plane ABM.