In an isosceles triangle ABC, points D and E are taken at the base of AC so that AD = CE.

In an isosceles triangle ABC, points D and E are taken at the base of AC so that AD = CE. Prove that triangle DBE is isosceles

Since triangle ABC is isosceles, its internal angles at the base of AC are equal, angle BAC = BCA, side AB = BC.

By condition, the segment AD = CE.

Then the triangles ABD and BCE are equal on two sides and the angle between them, which means BD = BE, and then the triangle DBE is isosceles, which was required to prove.




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