Question

На основании [AC] равнобедренного треугольника ABC отложены равные отрезки [AE] и [CD]. Докажите, что треугольники ABE и CDB равны.

Answer 1

Ответ:

Доказано

Объяснение:

Доказательство приведено на фото. Значок после доказательства (зачёркнутый квадрат – значок конца доказательства).

Надеюсь, было понятно.

Жду лучший ответ!

Answer 2

Given Information

We are given a triangle ABC, where AE and CD are equal segments that are drawn from the base of the triangle. We need to prove that triangles ABE and CDB are congruent.

Proof

To prove that triangles ABE and CDB are congruent, we can use the Side-Angle-Side (SAS) congruence criterion. According to this criterion, if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the two triangles are congruent.

In this case, we can see that: - Side AB is common to both triangles ABE and CDB. - Side AE is congruent to side CD (given). - Angle ABE is congruent to angle CDB because they are vertical angles.

Therefore, we have the following congruence: - Side AB is congruent to side AB (common side). - Side AE is congruent to side CD (given). - Angle ABE is congruent to angle CDB (vertical angles).

By the SAS congruence criterion, we can conclude that triangles ABE and CDB are congruent.

Conclusion

Triangles ABE and CDB are congruent based on the given information and the SAS congruence criterion.

Note: The sources provided did not contain specific information related to the given problem.