Question

Помогите пожалуйста, очень важно В параллелограмме MNKP диагональ МК равна 20см. Точки В и С - середины сторон NK и KP соответственно. Отрезок ВС пересекает диагональ МК в точке Е. Найдите МЕ и ЕК.

Answer 1

МЕ - ЕК = МК * 3/4 - МК * 1/4 = МК * 1/2 = 10 см

Answer 2

Parallelogram MNKP

In the given parallelogram MNKP, the diagonal MK is equal to 20 cm. Points B and C are the midpoints of sides NK and KP, respectively. Segment BC intersects the diagonal MK at point E. We need to find the lengths of ME and EK.

To find the lengths of ME and EK, we can use the properties of midpoints in a parallelogram.

Properties of Midpoints in a Parallelogram

In a parallelogram, the segment joining the midpoints of any two sides is parallel to and half the length of the diagonal it intersects.

Using this property, we can determine the lengths of ME and EK.

Length of ME

Since point B is the midpoint of side NK, we can conclude that segment BE is parallel to and half the length of diagonal MK. Therefore, the length of BE is 10 cm.

Similarly, since point C is the midpoint of side KP, segment CE is parallel to and half the length of diagonal MK. Therefore, the length of CE is also 10 cm.

Since segment BC intersects the diagonal MK at point E, we can conclude that segment ME is parallel to and half the length of diagonal MK. Therefore, the length of ME is also 10 cm.

Length of EK

To find the length of EK, we can subtract the length of ME from the length of MK.

Given that MK is 20 cm and ME is 10 cm, we can calculate the length of EK as follows:

EK = MK - ME = 20 cm - 10 cm = 10 cm

Therefore, the length of EK is 10 cm.

Final Answer

Based on the given information, we have determined that the length of ME is 10 cm and the length of EK is also 10 cm.