In an isosceles triangle ABC with base AC, bisectors AD and CF of equal angles CAB and ACB are drawn, respectively. prove that triangles ADB and CFB are equal.
Since the triangle is isosceles, then in triangles ADB and CFB, AB = CB.
CF and AD are the bisectors of the angles ACB and CAB, then the angle BAD = BCF. In triangles ADB and CFB, angle ABC is common.
Then the triangles ADB and CFB are equal in the side and the angles adjacent to it – according to the second sign of equality of triangles. Q.E.D.
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