Centroid

The centroid of a triangle is the point where the three medians of the triangle intersect. The median of a triangle is a line segment from a vertex to the midpoint of the opposite side.

Finding the Centroid

To find the centroid of a triangle, you can use the following steps:

1. Find the midpoint of each side of the triangle.
2. Draw a line from each vertex to the midpoint of the opposite side. These lines are the medians of the triangle.
3. The point where the three medians intersect is the centroid of the triangle.

Properties of the Centroid

Some important properties of the centroid include:

• The centroid divides each median into two segments, with the segment closer to the midpoint of the opposite side being twice as long as the other segment.
• The centroid is the center of mass of the triangle, meaning it is the point where the triangle would balance if it were cut out of a sheet of uniform material.

Practice Problems

1. Find the centroid of a triangle with vertices at (1, 2), (3, 4), and (5, 6).

2. In triangle ABC, the length of median AD is 6 cm. If D is the centroid of the triangle, find the length of BC.

Additional Resources

For more practice problems and in-depth explanations, check out the following resources:

• Khan Academy - Centroid of a triangle
• MathIsFun - Centroid of a triangle