The angle bisectors of a regular polygon are always concurrent. And the point that they meet at is also the meeting point of the perpendicular bisectors of the sides. If it is a polygon with an odd nmber of sides, the "medians" [line from vertex to mid-point of opposite side] and "altitudes" [perpendicular from vertex to opposite side] will also meet at the same point.
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You can find the intersection of the angle bisectors or the intersection of the perpendicular bisectors of each side.
A regular polygon triangle is an equilateral triangle. It has three lines of symmetry: a line passing through each vertex and the mid-point of the opposite side. These are the three medians or altitudes or perpendicular bisectors or angle bisectors of the triangle - they are all the same lines.
it is not a line segment
A 6 sided hexagon polygon can be regular or irregular.
Sometimes. By definition, a semi-regular tessellation must include more than one type of regular polygon. Some uniform tessellations use more than one type of regular polygon, but many uniform tessellations use only a single regular polygon. Therefore the statement is only sometimes true.