Question

Открезки AD и BC пересекаются их в общей середине точке M. Докажите, что прямые AC и BD параллельны

Answer 1

УголCAO=DBO............

Answer 2

Proof that lines AC and BD are parallel

To prove that lines AC and BD are parallel, we can use the fact that the line segments AD and BC intersect at their midpoint, point M.

Let's assume that lines AC and BD are not parallel. This means that they intersect at some point, let's call it P.

Since AD and BC intersect at their midpoint M, we can draw line segments AM, MD, BM, and MC. Now we have two triangles, triangle AMP and triangle BMP.

According to the Midpoint Theorem, line segment AM is equal in length to line segment MD, and line segment BM is equal in length to line segment MC.

Now, let's consider triangle AMP and triangle BMP. Since line segment AM is equal in length to line segment MD, and line segment BM is equal in length to line segment MC, we can conclude that triangle AMP is congruent to triangle BMP by the Side-Side-Side (SSS) congruence criterion.

If triangle AMP is congruent to triangle BMP, then angle AMP is congruent to angle BMP, and angle PMA is congruent to angle PMB.

Since angles PMA and PMB are congruent, they are alternate interior angles formed by the transversal line AC intersecting the lines AD and BC. According to the Alternate Interior Angles Theorem, if two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.

However, we assumed that lines AC and BD are not parallel, which means that the alternate interior angles PMA and PMB cannot be congruent. This is a contradiction.

Therefore, our assumption that lines AC and BD are not parallel must be false. Hence, lines AC and BD are parallel.

In conclusion, we have proved that lines AC and BD are parallel.