Question

prove that every point on the
perpendicular bisestor of a segment is equidistant from the endpoint of segment​

Answer 1

Answer:

Therefore, any point on the perpendicular bisector of a segment is the same distance from each endpoint. Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Step-by-step explanation:

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Answer 2

Answer:

Every point on the perpendicular bisector of a segment is equidistant from the ends of the segment

Therefore, any point on the perpendicular bisector of a segment is the same distance from each endpoint. Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

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Step-by-step explanation:

Perpendicular Bisectors

Intersect line segments at their midpoints and form 90 degree angles with them.

Perpendicular Bisectors

Imagine an archeologist in Cairo, Egypt, found three bones buried 4 meters, 7 meters, and 9 meters apart (to form a triangle)? The likelihood that more bones are in this area is very high. The archeologist wants to dig in an appropriate circle around these bones. If these bones are on the edge of the digging circle, where is the center of the circle? Can you determine how far apart each bone is from the center of the circle? What is this length? 



Perpendicular Bisectors

Recall that a perpendicular bisector intersects a line segment at its midpoint and is perpendicular. Let’s analyze this figure.



CD←→ is the perpendicular bisector of AB¯¯¯¯¯¯¯¯. If we were to draw in AC¯¯¯¯¯¯¯¯ and CB¯¯¯¯¯¯¯¯, we would find that they are equal. Therefore, any point on the perpendicular bisector of a segment is the same distance from each endpoint.

Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

In addition to the Perpendicular Bisector Theorem, we also know that its converse is true.

Perpendicular Bisector Theorem Converse: If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.

Proof of the Perpendicular Bisector Theorem Converse:



Given: AC¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯

Prove: CD←→ is the perpendicular bisector of AB¯¯¯¯¯¯¯¯

Statement