Question

71. Диагонали прямоугольника ABCD пересекаются в точке о Докажите, что треугольник AOD – равнобедренный, Помогите пожалуйста ​

Answer 1

Ответ:Диагонали прямоугольника равны между собой и при пересечении делятся пополам,поэтому

АО=DO

АО и DO являются боковыми сторонами треугольника АОD,значит-он равнобедренный

Объяснение:

Answer 2

Ответ:

У прямоугольника диагонали равны, значит АО=ВО=СО=DO

AOD=AO=DO-Равнобедренный

Объяснение:

Answer 3

Diagonal Intersection in Rectangle ABCD

To prove that triangle AOD is isosceles (or, in other words, that it is an isosceles triangle), we need to show that the lengths of AO and OD are equal.

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

- A: one of the vertices of the rectangle - B: the adjacent vertex to A - C: the opposite vertex to A - D: the adjacent vertex to C - O: the point of intersection of the diagonals

To prove that triangle AOD is isosceles, we need to show that AO = OD.

To do this, we can use the properties of rectangles and the fact that the diagonals of a rectangle bisect each other.

Proof:

1. In a rectangle, opposite sides are equal in length. Therefore, AB = CD and AD = BC. 2. The diagonals of a rectangle bisect each other. This means that the point of intersection O divides both diagonals in half. So, AO = OB and CO = OD. 3. Since AB = CD and AD = BC, we can rewrite AO = OB as AO = AB/2 and CO = OD as CO = CD/2. 4. Combining the above equations, we have AO = AB/2 = CD/2 = OD. 5. Therefore, AO = OD, which means that triangle AOD is isosceles.

In conclusion, we have proven that triangle AOD is isosceles because AO is equal to OD.

Please let me know if you need any further clarification or assistance.