Question

В трапеции АВСD боковые стороны АВ и СD равны, СН - высота, проведённая к большему основанию АD. Найдите длину отрезка НD, если средняя линия КМ трапеции равна 10, а меньшее основание ВС равно 4 Можно пожалуйста ответ с рисунком, дам 40 баллов

Answer 1

Ответ:

Объяснение:

Дано:

ABCD - трапеция

АВ = CD

ВС = 4

СН - высота

КМ = 10 (средняя линия: АК = КB, СМ = MD)

HD = ?

1) АВ = CD, т.е. трапеция - равнобедренная

2) Свойство трапеции: средняя линия трапеции параллельна основаниям и равна полусумме оснований:

КМ = (ВС + AD)/2

10 = (4 +AD)/2  →    20 = 4 + AD   →  AD = 20 -4   → AD = 16

3) Свойство равнобедренной трапеции:

Высота (CH), опущенная из вершины (C) на большее основание (AD), делит его на большой отрезок (AH), который равен полусумме оснований и меньший (HD), равный полуразности оснований:

HD = (AD - BC)/2 =  (16 - 4)/2 = 6

HD = 6.

Answer 2

Task: Finding the length of segment HD in trapezoid ABCD

To find the length of segment HD in trapezoid ABCD, we need to use the given information: - The lengths of the lateral sides AB and CD are equal. - SN is the height of the trapezoid, drawn from the larger base AD. - The length of the median KM of the trapezoid is 10. - The length of the smaller base BC is 4.

Let's break down the problem step by step.

Step 1: Understanding the trapezoid and its properties

A trapezoid is a quadrilateral with one pair of parallel sides. In trapezoid ABCD, AB and CD are the parallel sides, and AD and BC are the non-parallel sides. SN is the height of the trapezoid, drawn from the larger base AD.

Step 2: Using the properties of a trapezoid

In a trapezoid, the median is the line segment connecting the midpoints of the non-parallel sides. In trapezoid ABCD, the median KM is given as 10.

Step 3: Applying the properties to find the length of HD

To find the length of HD, we can use the property that the median of a trapezoid divides the height into two equal segments. Therefore, we can conclude that HN is equal to ND.

Let's denote the length of HN and ND as x.

Since the median KM is given as 10, we can write the equation:

2x + 4 = 10

Simplifying the equation, we get:

2x = 6

Dividing both sides by 2, we find:

x = 3

Therefore, the length of HD (which is equal to HN and ND) is 3.

Step 4: Visual representation

Here is a visual representation of trapezoid ABCD with the given information:

       A _________ B
        /         \
       /           \
      /             \
     /               \
    /                 \
   D_________________ C

In this trapezoid, AB and CD are the parallel sides, AD and BC are the non-parallel sides, SN is the height, and KM is the median.

The length of HD (HN and ND) is 3.

I hope this explanation helps! If you have any further questions, please let me know.