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Q: What does it mean that points in the interior of angle ABC and equidistant from the sides of angle ABC?

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(The set of all points equidistant from the two sides of the angle. :)

The bisector of that angle.

Bisector (apex)

Angle bisectors are.

Every point on the bisector of an angle is equidistant from the sides of that angle. It is understood that the distance of a point from a line is the length of the perpendicular dropped from the point to the line.

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A line that is the angle bisector.

Bisector of an angle, is defined as the set of all points in a plane that are equidistant from the two sides of a given angle.

(The set of all points equidistant from the two sides of the angle. :)

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The bisector of that angle.

angle bisector

angle bisector

The set of all points in a plane that are equidistant from the two sides of a given angle

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle-apex

Equidistant from the two sides of an angle.

Yes it is, if the point isn't equidistant from both sides, then it cannot be on the angle bisector.

Bisector (apex)