SOLUTION: what is the proof for proving the line segment from the centerpoint of a regular polygon bisects each interior angle of the polygon.
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Question 315319: what is the proof for proving the line segment from the centerpoint of a regular polygon bisects each interior angle of the polygon.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You cannot prove "the line segment from the centerpoint of a regular polygon bisects each interior angle of the polygon." It simply is not true, at least not stated in that fashion. That is because "the" line segment is singular, as in one single line segment. One line segment that has an endpoint at the center of the polygon can only possibly bisect one of the polygon's many (c.f. definition of 'poly') vertices, and then only if the other endpoint of the segment were the vertex itself.
It is true that any line segment that has end points at the center of a regular polygon and at one of the vertices of that polygon bisects the internal angle of the polygon at the connected vertex. You would simply show that for any n-gon if you connect ALL of the vertices with the center of the n-gon you will have created n congruent isosceles triangles because the radial line segments are radii of a circumscribed circle and therefore equal in measure and each of the triangles has a third side formed by the equal length sides of a regular polygon (c.f. definition of a regular polygon) from which it directly follows that each of the radial segments is a bisector because any two adjacent angles around the interior perimeter of the polygon must be equal.
But that isn't what you asked.
John
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