Question

Точка e не лежит в плоскости параллелограмма abcd. докажите, что прямая, проходящая через середины отрезков ea и eb, параллельна стороне cd

Answer 1

Доказательнство,

1)прямая KF- средняя линия в треугольнике АЕВ ( так как К-середина отрезка ЕА, а F-середина ЕВ)

2)следовательно KF||FB-по свойству средней линиии(средняя линия в треугольнике параллельна основанию треугольника)

3) ТАк как AB|| CD( по свойству параллелограмма), а KF||AB то KF||CD

что и требовалось доказать!

Answer 2

Statement:

Точка e не лежит в плоскости параллелограмма ABCD. Докажите, что прямая, проходящая через середины отрезков ea и eb, параллельна стороне cd.

Proof:

To prove that the line passing through the midpoints of segments ea and eb is parallel to side cd, we can use the concept of midpoints and parallel lines.

Let's assume that the midpoint of segment ea is M and the midpoint of segment eb is N. We need to show that MN is parallel to cd.

According to the midpoint theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.

In this case, we can consider triangle AEB. The midpoints of ea and eb are M and N, respectively. Therefore, MN is parallel to AB and its length is half of AB.

Now, let's consider the parallelogram ABCD. Since MN is parallel to AB, it is also parallel to CD, as opposite sides of a parallelogram are parallel.

Therefore, we have proved that the line passing through the midpoints of segments ea and eb, MN, is parallel to side cd.

Note: The proof provided above is a logical deduction based on the given information. It does not rely on specific numerical values or coordinates of the points involved.