Question

Отрезки АВ и СД пересекаются в точке Р и делятся пополам. Докажите, что АС II ВД

Answer 1

Ровно или параллельно?
Рассмотрим треугольник АСР и РВД они равны за двумя сторонами и углом между ними(уголСРА=углуВРД как вертикальные)
Так, как треугольники равны, равны соответствующие элементы СА=ВД

Answer 2

Given Information:

We are given that line segments AB and CD intersect at point P and divide each other in half. We need to prove that AC is parallel to BD.

Proof:

To prove that AC is parallel to BD, we can use the concept of alternate interior angles. If AC is parallel to BD, then the alternate interior angles formed by the intersection of AB and CD should be equal.

Let's consider the alternate interior angles formed by the intersection of AB and CD at point P. Let angle APB be x and angle CPD be y.

According to the given information, line segments AB and CD divide each other in half. This means that the angles formed by the intersection of AB and CD are equal. Therefore, angle APB is equal to angle CPD.

Since angle APB is equal to angle CPD, we can conclude that AC is parallel to BD.

Therefore, we have proved that AC is parallel to BD.

Note: Unfortunately, I couldn't find specific search snippets to cite for this proof. However, the concept of alternate interior angles is a well-known geometric concept that can be found in various geometry textbooks and resources.