Question

Параллелограммы ABCD иABC1D1 лежат в разных плоскостях.Докажите,что CDD1C1-параллелограмм.

Answer 1

Поскольку CD и C1D1 параллельны и равны, то очевидно CD C1D1 паралелограмм

Answer 2

Proof that CDD1C1 is a parallelogram

To prove that CDD1C1 is a parallelogram, we need to show that its opposite sides are parallel.

Let's consider the parallelogram ABCD and ABC1D1. Since these two parallelograms lie in different planes, we cannot directly compare their sides. However, we can use the information provided to establish the relationship between the sides of CDD1C1.

From the given information, we know that ABCD and ABC1D1 are parallelograms. Therefore, their opposite sides are parallel. Let's denote the sides of ABCD as AB, BC, CD, and DA, and the sides of ABC1D1 as AB, BC1, C1D1, and DA.

Now, let's focus on the sides of CDD1C1. We can see that CD and C1D1 are corresponding sides of the parallelograms ABCD and ABC1D1, respectively. Since the corresponding sides of two parallel lines are also parallel, we can conclude that CD and C1D1 are parallel.

Similarly, we can observe that CC1 and DD1 are opposite sides of the parallelograms ABCD and ABC1D1, respectively. Since the opposite sides of a parallelogram are parallel, we can conclude that CC1 and DD1 are parallel.

Therefore, we have shown that the opposite sides of CDD1C1, namely CD and C1D1, as well as CC1 and DD1, are parallel. Hence, CDD1C1 is a parallelogram.

Note: The proof provided above is based on the information given in the question. If you need a more detailed or mathematical proof, please let me know.