Question

In a $\Delta$ABC D, E, F are midpoints of sides BC, AC, AB respectively. If D, E, F are joined to A, B, C respectively to meet at a common point G, then select the correct options.

• A. There are 6 triangles formed with G as one of the vertex.
• B. G is the centroid of the triangle.
• C. GD is a part of median.
• D. BGC is a triangle.

Answer 1

Answer: (B), (C), (D)

The correct options are
B G is the centroid of the triangle.
C GD is a part of median.
D BGC is a triangle.


New triangles formed with G as one of the vertex are 9, which are $\Delta$AGF, $\Delta$BGF, $\Delta$AGB, $\Delta$BGD, $\Delta$DGC, $\Delta$BGC, $\Delta$CGE, $\Delta$EGA and $\Delta$CGA.

G is centroid formed by the intersection of medians AD, BE and FC. We can see that GD is the part of the median AD. $\Delta$BGC is a triangle newly formed.