Question

Стороны параллелограмма равны 12 и 9 см. Биссектрисы двух углов, прилежащих к большей стороне параллелограмма, делят противоположную сторону на три отрезка. Найдите длины этих отрезков. ПОМОГИТЕ, ПОЖАЛУЙСТА!

Answer 1

Биссектрисы углов отсекают равнобедренные треугольники с каждой стороны. Т.к. сумма отсеченных отрезков на большей стороне параллелограмма 9+9=18 и больше самой стороны, которая равна 12, то биссектрисы пересекаются. Отсюда отрезки крайние - по 3, средний - 6.

Answer 2

Parallelogram and Bisectors

To find the lengths of the segments that the bisectors of the angles adjacent to the longer side of a parallelogram divide the opposite side into, we can use the properties of parallelograms.

Let's denote the longer side of the parallelogram as AB and the opposite side as CD. The bisectors of the angles adjacent to side AB divide side CD into three segments, let's call them CE, EF, and FD.

To find the lengths of these segments, we need to use the fact that the opposite sides of a parallelogram are congruent. In other words, AB = CD.

Since we know that the lengths of the sides of the parallelogram are 12 cm and 9 cm, we can set up the following equation:

AB = CD

12 = CE + EF + FD

Now, let's solve for the lengths of the segments CE, EF, and FD.

Solving for the Lengths of the Segments

To find the lengths of the segments CE, EF, and FD, we need to use the fact that the bisectors divide the opposite side into three equal parts.

Let's assume that CE = EF = FD = x.

Using this assumption, we can rewrite the equation as:

12 = x + x + x

Simplifying the equation, we get:

12 = 3x

Dividing both sides of the equation by 3, we find:

x = 4

Therefore, the lengths of the segments CE, EF, and FD are all equal to 4 cm.

Summary

In summary, the lengths of the segments that the bisectors of the angles adjacent to the longer side of the parallelogram divide the opposite side into are all equal to 4 cm.

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