Question

На рисунке точка К является серединой отрезков АD и BC.Докажите,что прямые АB и CD параллельны

Answer 1

Так как чтобы точка К являлась серидиной 2 отрезков создаётся крест из отрезков. А это значит что AB и CD являются параллельны

Answer 2

Given Information:

On the given figure, point K is the midpoint of segments AD and BC. We need to prove that lines AB and CD are parallel.

Proof:

To prove that lines AB and CD are parallel, we can use the midpoint theorem. According to the midpoint theorem, if a line segment has a midpoint, then it divides the segment into two equal parts.

Let's consider the line segment AD. Since K is the midpoint of AD, we can say that AK is equal to KD. Similarly, since K is the midpoint of BC, we can say that BK is equal to KC.

Now, let's compare the lengths of the line segments AB and CD. Since AK = KD and BK = KC, we can conclude that AK + BK = KD + KC. This can be simplified to AB = CD.

Therefore, we have shown that AB = CD, which means that the line segments AB and CD are equal in length.

Now, let's consider the angles formed by these line segments. Since AB = CD and the opposite sides of a parallelogram are equal, we can say that angle ABC is equal to angle CDA.

Therefore, we have shown that AB = CD and angle ABC = angle CDA. According to the definition of parallel lines, if two lines have equal corresponding angles, then they are parallel.

Hence, we can conclude that lines AB and CD are parallel.

Note: The proof provided above is based on the given information and the application of the midpoint theorem.