Question

Сторона AB параллелограмма ABCD вдвое больше стороны BC .точка m середина высоты AB.Докажите что биссектриса угла BCD. ПОМОГИТЕ ПОЖАЛУЙСТА

Answer 1

Дано:
Параллелограмм ABCD
AB=2BC
m-середина высота AB
Док-во:
AH=BH=1/2AB=BC
треугольник BCH равнобедренный
угол BHC= угол BCH, но угол BHC= угол HCD как внутренние разносторонние 
тогда угол BCH= угол HCD, СH - биссектриса угла 

Answer 2

Given Information

We are given that side AB of parallelogram ABCD is twice as long as side BC, and point M is the midpoint of height AB.

To Prove

We need to prove that the bisector of angle BCD passes through point M.

Proof

To prove that the bisector of angle BCD passes through point M, we can use the properties of parallelograms and the given information.

Let's consider the following diagram:

     A _______ B
      |\     /|
      | \   / |
      |  \ /  |
      |   X   |
      |  / \  |
      | /   \ |
      |/_____\|
     D         C

Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Therefore, AB = CD and BC = AD.

Given that AB is twice as long as BC, we have AB = 2BC.

We are also given that point M is the midpoint of height AB. This means that AM = MB.

Now, let's consider triangle ABC. Since AB = 2BC and AM = MB, we can conclude that AM is equal to BC.

Since AM = BC, we can conclude that triangle ABC is an isosceles triangle.

In an isosceles triangle, the bisector of the base angle passes through the midpoint of the base. In this case, the base angle is angle BCD, and the midpoint of the base is point M.

Therefore, we can conclude that the bisector of angle BCD passes through point M.

Conclusion

We have proved that the bisector of angle BCD passes through point M, using the properties of parallelograms and the given information.

Please let me know if I can help you with anything else.