Question

Помогите плиз!! Срочно!!!! Точка О – середина отрезка АВ, а точка S лежит на прямой АВ вне данного отрезка. Докажите, что длина отрезка OS равна полусумме длин отрезков AS и BS.

Answer 1

Ответ:

Объяснение:

Взять отрезки равные отрезки за Х (AO, OB), и отрезок BS за y. Подставить в то, что надо доказать

Answer 2

To prove that the length of segment OS is equal to half the sum of the lengths of segments AS and BS, we can use the midpoint theorem. The midpoint theorem states that if a point S lies on a line segment AB, dividing it into two equal parts, then the line segment OS is parallel to AB and is equal to half the length of AB.

Midpoint Theorem

According to the midpoint theorem, if a point S lies on a line segment AB, dividing it into two equal parts, then the line segment OS is parallel to AB and is equal to half the length of AB.

To apply the midpoint theorem to this problem, we need to show that point S is the midpoint of segment AB.

Proof

Given: - Point S lies on line segment AB, but outside the segment. - Point O is the midpoint of segment AB.

To prove: - The length of segment OS is equal to half the sum of the lengths of segments AS and BS.

Proof by contradiction: Assume that the length of segment OS is not equal to half the sum of the lengths of segments AS and BS.

Let's consider the case where the length of segment OS is greater than half the sum of the lengths of segments AS and BS. In this case, point S would be closer to point B than to point A.

If point S is closer to point B, then the length of segment BS would be greater than the length of segment AS. This contradicts the fact that point O is the midpoint of segment AB.

Similarly, if we consider the case where the length of segment OS is less than half the sum of the lengths of segments AS and BS, point S would be closer to point A than to point B. In this case, the length of segment AS would be greater than the length of segment BS,