medians-3 altitudes-3
Two points determine a unique line. Therefore, there are infinitely many circles that can pass through two given points. This is because a circle can be defined by its center, which can lie anywhere along the perpendicular bisector of the line segment connecting the two points.
A line segment has exactly two endpoints. If it had less, then it would just be a point. If it was more, then it wouldn't be a segment anymore.
Normally just the the one which is in the middle of the line segment
There are infinitely many lines perpendicular to this line. All of them have the slope of -4/3, if that fact is of any help to you.
Exactly one. No more, no less.
Since there is no such word as "perpindicuar", it is difficult to be sure. A line segment can have only one perpendicular bisector.
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All bisectors intersect the line segment at the midpoint. There can be multiple bisectors, intersecting at the midpoint at different angles, but they all intersect the line segment at its midpoint. The midpoint separates the line segment into two equal halves.
A bisector is a line (or line segment) which passes through the midpoint. You can have multiple lines intersect at this one point, and all of them will bisect the original line segment, since they pass through its midpoint. A perpendicular bisector passes through the midpoint, and also is perpendicular to the original line segment, so there will be only one of those.
Equilateral triangles have 3 perpendicular bisectors
Explain why a line segment can have one midpoint but many bisectors
no-- It only has one. Since it is a segment, it has a definite start and end, so it has only one middle (the bisector).
Infinitely many. Each line segment contains one point which bisects it. Any one of the infinite lines through that point, apart from the original line, is a bisector.
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