In isosceles triangle ABC with base AC, the bisectors of angles A and C meet at point O.
| May 29, 2021 | education
In isosceles triangle ABC with base AC, the bisectors of angles A and C meet at point O. Prove that triangle AOC is isosceles.
Since, by condition, the triangle ABC is isosceles, then its angles located at the base of the AC are equal. Angle BAC = BCA.
AA1 and CC1 are the bisectors of the angles that they divide in half, then the angle A1AC = C1CA, and therefore, in the AOC triangle, the angle OAC = OCA, and then the AOC triangle is isosceles with the base AC, which was required to be proved.
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