Question

Діагоналі прямокутника ABCD перетинаються в точці О. Доведи,що трикутник AOB і АОD рівнобедрений​

Answer 1

Объяснение:  Диагонали в точке пересечения O делиться по-равну, следовательно в треугольнике AOB стороны BO и AO равны, и также в треугольнике AOD стороны AO и DO равны - треугольники равнобедренный

Answer 2

Diagonal Intersection in a Rectangle

To prove that triangle AOB and triangle AOD are isosceles (or "ravnobedrennyy" in Ukrainian), we need to show that the lengths of their sides are equal.

Let's consider rectangle ABCD, where the diagonals intersect at point O. We can label the sides of the rectangle as follows:

- AB and CD are the longer sides of the rectangle. - AD and BC are the shorter sides of the rectangle.

Now, let's examine triangle AOB. The sides of this triangle are AO, OB, and AB. Since AO and OB are the diagonals of the rectangle, we know that they are equal in length. This is because the diagonals of a rectangle bisect each other and are congruent.

Therefore, we can conclude that triangle AOB is an isosceles triangle because AO = OB.

Similarly, let's consider triangle AOD. The sides of this triangle are AO, OD, and AD. Again, since AO is a diagonal of the rectangle, it is equal in length to OD. Therefore, triangle AOD is also an isosceles triangle because AO = OD.

In summary, we have shown that both triangle AOB and triangle AOD are isosceles triangles because two of their sides are equal in length.

I hope this explanation helps! Let me know if you have any further questions.