The point where the three angle bisectors of an equilateral triangle intersect is called the centroid. In the provided image, labeled as point K, it is located two-thirds of the distance from each vertex to the midpoint of the opposite side.
The point of intersection of the three angle bisectors of an equilateral triangle is called the **centroid** of the triangle. The centroid is located two-thirds of the distance from each vertex to the midpoint of the opposite side.
[Image of equilateral triangle with centroid]
In the image you provided, the centroid of triangle GHI is labeled point K. To see this, we can use the following properties of equilateral triangles:
* All three angles of an equilateral triangle measure 60 degrees.
* The three medians of an equilateral triangle are also angle bisectors.
* The three medians of an equilateral triangle intersect at a point two-thirds of the distance from each vertex to the midpoint of the opposite side.
Since triangle GHI is equilateral, we know that the three angle bisectors are also medians. Therefore, the three angle bisectors intersect at the centroid of the triangle.
To summarize, the point of intersection of the three angle bisectors of an equilateral triangle is the centroid of the triangle, which is labeled point K in the image you provided.