Centroids of Triangles Worksheet

Centroids of Triangles

Read each question carefully and provide clear, concise answers. Show all your work for calculations.

1. A   of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

2. The point of concurrency of the three medians of a triangle is called the  .

3. The centroid divides each median in a   ratio.

4. If G is the centroid of triangle ABC and AD is a median, which of the following statements is true?

5. The coordinates of the vertices of a triangle are A(0, 0), B(6, 0), and C(3, 9). What are the coordinates of its centroid?

6. In triangle PQR, median PS has a length of 18 cm. If G is the centroid, find the lengths of PG and GS.

7. The vertices of a triangle are D(1, 4), E(7, 2), and F(4, 9). Calculate the coordinates of the centroid of triangle DEF.

8. The centroid of a triangle is always inside the triangle.

9. The centroid is equidistant from all three vertices of the triangle.

10. Observe the triangle ABC with medians AD, BE, and CF intersecting at centroid G.

a) If AD = 21 cm, what is the length of AG?  

b) If GE = 5 cm, what is the length of BE?  

c) If GC = 10 cm, what is the length of CF?