Question

Отрезки АВ и СД пересекаются в их середине точке М. Докажите, что АС параллельна ДВ.

Answer 1

AMB=CMD 
AC//DB
значит они паралельны

Answer 2

Given Information

The given information states that line segments AB and CD intersect at their midpoint M, and the task is to prove that AC is parallel to BD.

Proof

To prove that AC is parallel to BD, we can use the property that if a line segment is drawn through the midpoint of another line segment and is parallel to a third line segment, then it divides the third line segment into two equal parts.

Given: - Line segments AB and CD intersect at their midpoint M.

To prove: - AC is parallel to BD.

Proof: - Since AB and CD intersect at their midpoint M, it follows that AM = MB and CM = MD. - Now, consider the triangles AMC and BMD. - By the property of midpoints, AM = MB and CM = MD. - Therefore, triangle AMC is congruent to triangle BMD by the Side-Side-Side (SSS) congruence criterion. - By the corresponding parts of congruent triangles, it follows that AC is parallel to BD.

Therefore, AC is parallel to BD.

Conclusion

The proof demonstrates that line segment AC is parallel to line segment BD, given that line segments AB and CD intersect at their midpoint M.