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In general, they are not. In an isosceles triangle, the perpendicular bisector of the base is the same as the bisector of the angle opposite the base. But the other two perp bisectors are not the same as the angle bisectors. Only in an equilateral triangle is each perp bisector the same as the angle bisector of the angle opposite.

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Q: How are perpendicular bisectors and angle bisectors the same?
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