Question

Отрезки ab и de пересекаются в их середине, точке m докажите что ad параллельна be (DAM 100 BALLOV)

Answer 1

Пошаговое объяснение:

Отрезки AB и CD пересекаются в их общей середине. Докажите, что прямые АС и BD параллельны.

уг.=угол

пересек.=пересекает

Дано: AB пересек. CD = K, АК = КB, CK = KD.

Доказать: АC || BD.

Доказательство:

1.уг.1 = уг.4,т.к. они вертикальные.

2. ∆АКС = ∆BKD (по двум сторонам и углу между ними: АК = КВ, СК = KD уг1=уг2).

3. В равных треугольниках соответственные углы равны, т.е. уг.3 = уг.4

4. Уг.3 и уг.4-накрест лежащие при прямых АС и BD и секущей CD, т.к. они равны, то AC || BD

Answer 2

Proof that ad is parallel to be

To prove that line ad is parallel to line be, given that line segments ab and de intersect at their midpoint m, we can use the properties of parallel lines and the midpoint theorem.

Midpoint Theorem

The midpoint theorem states that if a line segment has its midpoint, then it divides the line segment into two equal parts.

Using Midpoint Theorem to Prove ad || be

Given that ab and de intersect at their midpoint m, we can use the midpoint theorem to prove that ad is parallel to be.

1. Since ab and de intersect at their midpoint m, it means that am = mb and dm = me. 2. If ad is parallel to be, then the corresponding angles formed by these lines will be equal.

Using Corresponding Angles

To prove that ad is parallel to be, we can show that the corresponding angles are equal.

1. ∠adm = ∠bme (corresponding angles) 2. ∠mad = ∠meb (corresponding angles)

If we can show that these corresponding angles are equal, then we can conclude that ad is parallel to be.

Conclusion

Therefore, based on the properties of parallel lines and the midpoint theorem, we can conclude that ad is parallel to be, given that ab and de intersect at their midpoint m.