Why is it possible that angle bisector of the vertex of isosceles triangle perpendicular to the base?

an isosceles triangle can have any vertex angle less than 180 and greater than 0, as long the other two angles are equal. an isosceles triangle with a vertex of 179 degrees would just have the other two angles be 0.5 degrees. A right triangle with matching angles (both 45 degrees) would be both a right triangle and isosceles triangle.

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