Question

Дано: Треугольник СDE CEбисектрисса доказать DE||CB СРООООЧНООО!!!!​

Answer 1

Ответ:

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Answer 2

Given Information:

We are given that triangle CDE has CE as the angle bisector. We need to prove that DE is parallel to CB.

Proof:

To prove that DE is parallel to CB, we can make use of the angle bisector theorem. According to this theorem, if a line divides an angle of a triangle into two equal angles, then it divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

In triangle CDE, we have CE as the angle bisector. Let's denote the length of CD as a, the length of CE as b, and the length of DE as c.

According to the angle bisector theorem, we have:

CE/ED = CD/DE

Now, let's consider triangle CBE. Since DE is parallel to CB, we can apply the intercept theorem. According to the intercept theorem, if two lines are parallel, then the segments they intercept on any transversal are proportional.

Therefore, we have:

CE/ED = CB/BE

Combining the two equations, we get:

CD/DE = CB/BE

Since we know that CE is the angle bisector, we can also say that:

CD/CE = DE/BE

Now, let's compare the two equations:

CD/DE = CB/BE

CD/CE = DE/BE

We can see that the left-hand sides of the two equations are equal, and the right-hand sides are also equal. Therefore, we can conclude that the two lines DE and CB are parallel.

Thus, we have proved that DE is parallel to CB.

Please let me know if you have any further questions!