Question

Select all the true statements below.

Question 22 options:

The intersection of the three medians of a triangles is called a centroid.


An angle bisector divides an angle into three equal parts.


The centroid is called a point of balance or the center of the triangle.


Perpendicular bisectors intersect at a point called the incenter.

Answer 1

Let's evaluate each statement one by one:

1. **The intersection of the three medians of a triangle is called a centroid.**
- **True.** The centroid is indeed the point where the three medians of a triangle intersect.

2. **An angle bisector divides an angle into three equal parts.**
- **False.** An angle bisector divides an angle into two equal parts, not three.

3. **The centroid is called a point of balance or the center of the triangle.**
- **True.** The centroid is often referred to as the "center" or "balance point" of the triangle because it is the point where the mass of the triangle would balance.

4. **Perpendicular bisectors intersect at a point called the incenter.**
- **False.** The perpendicular bisectors of a triangle intersect at a point called the circumcenter, not the incenter. The incenter is formed by the intersection of the angle bisectors of a triangle.

Based on this analysis, the true statements are:

- The intersection of the three medians of a triangle is called a centroid.
- The centroid is called a point of balance or the center of the triangle.