Question

В пароллелограмме ABCD стороны равны AB=8 и BC=11.Биссектриса угла ABC пересекает сторону AD в точке L. Найдите AL?

Answer 1

Пусть ABCD параллелограмм и BL- биссектриса тогда угол АВL= углу СВL.

Угол СВL=углу АLВ как внутренние накрест лежащие

при паралельных ВС и АD и секущей ВL. Тогда треуг-к АВL - равнобедренный

отсюда АВ=АL=8см

Answer 2

Given Information:

We are given a parallelogram ABCD with sides AB = 8 and BC = 11. The angle bisector of angle ABC intersects side AD at point L. We need to find the length of AL.

Solution:

To find the length of AL, we can use the angle bisector theorem, which states that in a triangle, the angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.

In this case, we have triangle ABC with angle bisector BL. Let's denote the length of AL as x. According to the angle bisector theorem, we have:

AL / AD = BL / BD

Since ABCD is a parallelogram, AD is parallel to BC, and therefore, BD = BC = 11. Substituting the given values, we have:

x / 8 = BL / 11

To find BL, we can use the fact that the angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides. In this case, BL is proportional to AB and BC. Since ABCD is a parallelogram, AB = CD = 8. Therefore, we have:

BL / AB = BC / CD

Substituting the given values, we have:

BL / 8 = 11 / 8

Simplifying, we find:

BL = 11/8 * 8 = 11

Now, we can substitute the value of BL into the equation we obtained earlier:

x / 8 = 11 / 11

Simplifying, we find:

x = 8

Therefore, the length of AL is 8.