Based on the Prepswift videos, it seems that a radius drawn from the center of an equilateral triangle to any vertex divides that vertex angle into half (acts as an angle bisector).
Is this also true for other regular polygons and non-regular polygons?
Does anyone have a summary of all properties around this concept that can be tested on the GRE?
When I asked GPT-5, it said only equilateral triangles have this property. When I asked GPT-5 Thinking, it said all regular polygons have this property. I did not get any great answers via simple Google Search
Just so that I am understanding it correctly, it follows directly from the property that a n-sided regular polygon can be divided into (n - 2) congruent triangles, right?
You can split a regular polygon with n sides into n congruent isosceles triangle. Each interior angle is made up of two base angles from these triangles. Because all the triangles are congruent, their base angles are equal. As such, the line connecting a vertex to the center is an angle bisector of each interior angle.
