Properties of the median
- The centroid divides each median in the ratio AG:GM=2 (from vertex to base).
- The three larger triangles with vertex at G and sides along the vertices of the original triangle have equal areas:
1.
In triangle ABC, M is the midpoint of BC. Prove that .
2.
In triangle ABC, M is the midpoint of BC. If =24, find
3.
In triangle ABC, let G be the centroid. If , ..................
4.
In triangle ABC, let G be the centroid. If , the area of the triangle BCG is: .........
5.
Construct the medians BN and CP. Find the ratio of the areas of triangles GNC and GAP.