# In an isosceles triangle ABC with base AB, bisectors AA1 and BB1 are drawn. Prove that triangle ABA1

July 23, 2021 | education

| **In an isosceles triangle ABC with base AB, bisectors AA1 and BB1 are drawn. Prove that triangle ABA1 is equal to triangle ABB1.**

In an isosceles triangle, the angles at the base are equal, the angle CAB = CBA. Since AA1 and BB1 are bisectors of equal angles, the angle CAA1 = BAA1 = CBB1 = ABB1.

In triangles ABA1 and ABB1, side AB is common, angle ABB1 = BAA1, and angle ABA1 = BAB1. Then triangle ABA1 is equal to triangle ABB1 along the side and two adjacent corners, according to the second criterion of equality of triangles, which was required to prove.

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