Question

На сторонах угла B отложены равные отрезки BA и BC и отмечены точки Е и D так, что угол BEC равен углу ADB. Найдите длину EС, если AD = 4 см. Можно с решением (желательно),срочно надо ,помогите пжл

Answer 1

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Answer 2

Problem Analysis

We are given a quadrilateral ABCD, where AB = BC and AD = 4 cm. Points E and D are marked on the sides BA and BC, respectively, such that angle BEC is equal to angle ADB. We need to find the length of EC.

Solution

To solve this problem, we can use the fact that the sum of the angles in a quadrilateral is equal to 360 degrees. Let's denote angle BEC as x. Since angle BEC is equal to angle ADB, we can also denote angle ADB as x.

Using the fact that the sum of the angles in a triangle is equal to 180 degrees, we can find the measures of angles A and C in triangle ABC. Since AB = BC, angles A and C are equal. Let's denote the measure of angle A (and angle C) as y.

Now, we can write the following equations: 1. x + y + y + x = 360 (sum of angles in quadrilateral ABCD) 2. y + y + x = 180 (sum of angles in triangle ABC)

Simplifying equation 1, we get: 2x + 2y = 360 x + y = 180

Subtracting equation 2 from equation 1, we get: x = 180

Now, we can substitute the value of x into equation 2 to find the value of y: 180 + y = 180 y = 0

Since y = 0, this means that triangle ABC is degenerate, which implies that points A, B, and C are collinear. In this case, the length of EC is equal to the length of BC, which is equal to AB.

Given that AD = 4 cm, we can conclude that EC = AB = 4 cm.

Therefore, the length of EC is 4 cm.

Answer

The length of EC is 4 cm.