Question

площина а. що паралельна діагоналі ВD паралелограма АВСD перетинає йог суміжні сторони ВС і СD відповідно в точках М і N. обгрунтуйте розміщення МN і ВD. обчисліть довжину відрізка МN, якщо ВМ/MC= 2/3, а ВD= 15 см.

Answer 1

Плоскость α параллельная диагонали ВD параллелограмма АВСD пересекает его смежные стороны ВС и СD соответственно в точках М и N. Обоснуйте размещение МN и ВD. вычислите длину отрезка МN, если ВМ/MC= 2/3, а ВD= 15 см.

Объяснение:

Тк плоскость α ║ВD , то линия пересечения плоскостей α и (АВС) , будет параллельна BD ,те MN║BD.

ΔBCD~ΔMCN  по 2 -м углам : ∠С-общий , ∠CMN=∠CBD как соответственные ⇒ сходственные стороны пропорциональны

$\frac{BD}{MN} =\frac{BC}{MC} ,$  $\frac{15}{MN} =\frac{5}{3}$  ⇒ MN=9 cм.

Answer 2

Definition of a Parallelogram

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. In a parallelogram, the opposite angles are also equal.

Intersection of a Line Parallel to a Diagonal in a Parallelogram

In the given problem, we have a parallelogram ABCD. We are told that there is a line MN that is parallel to the diagonal BD and intersects the adjacent sides BC and CD at points M and N respectively. We need to determine the position of MN and calculate its length.

Position of MN and BD

Since MN is parallel to the diagonal BD, we can conclude that MN divides the parallelogram ABCD into two smaller parallelograms. Let's call the smaller parallelograms ABMN and MNCB.

Calculation of MN Length

To calculate the length of MN, we need to find the length of BD. We are given that BD = 15 cm.

To determine the length of MN, we need to find the ratio of the lengths of BM and MC. We are given that BM/MC = 2/3.

Using this information, we can set up the following equation:

BM + MC = BD

Substituting the given values, we have:

2x + 3x = 15

Simplifying the equation, we get:

5x = 15

Dividing both sides by 5, we find:

x = 3

Therefore, BM = 2x = 2 * 3 = 6 cm and MC = 3x = 3 * 3 = 9 cm.

Now, we can calculate the length of MN by subtracting BM from BC:

MN = BC - BM = 15 - 6 = 9 cm.

Conclusion

In the parallelogram ABCD, the line MN, which is parallel to the diagonal BD, intersects the adjacent sides BC and CD at points M and N respectively. The length of MN is 9 cm.