Question

Отрезки AB и cd пересекаются в их середине o докажите что ac||Bd

Answer 1

Строим четырёхугольник ACBD.
Из свойства пересечения диагоналей b деления в точке пересечения пополам, этот четырёхугольник - параллелограмм. 
Из свойств параллелограмма - противолежащие стороны параллельны. 

Answer 2

Given Information

We are given that the line segments AB and CD intersect at their midpoint O. We need to prove that AC is parallel to BD.

Proof

To prove that AC is parallel to BD, we can use the concept of midpoints and parallel lines.

Since O is the midpoint of both AB and CD, we can say that AO is equal to BO and CO is equal to DO. This is because the midpoint of a line segment divides it into two equal parts.

Now, let's consider the triangles AOC and BOD. We know that AO is equal to BO and CO is equal to DO. Additionally, the side AC is common to both triangles.

By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle AOC is congruent to triangle BOD.

When two triangles are congruent, their corresponding angles are equal. Therefore, angle AOC is equal to angle BOD.

Now, let's consider the alternate interior angles formed by the transversal line AC and the lines AB and CD. Angle AOC and angle BOD are alternate interior angles.

According to the Alternate Interior Angles Theorem, if two parallel lines are intersected by a transversal, then the alternate interior angles are equal.

Since angle AOC is equal to angle BOD, and they are alternate interior angles, we can conclude that AC is parallel to BD.

Therefore, we have proved that AC is parallel to BD.

Note: The given information and proof are based on the assumption that the line segments AB and CD intersect at their midpoint O. If there is any additional information or context, please provide it for a more accurate response.