The lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

The fout lines drawing from the vertices of any tetrahedron to the centroid to the centroid of the opposite faces meet in a point whose distance from each vertex is 'k' times the distance from each vertex to the opposite face, where k is

Show that the segments joining vertices to the centroid of opposite faces of a tetrahedron are concurren Hence find the position vector of the point of concurrence.

Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

Medians the line segments joining the vertices to the mid-points of the opposite side of a triangle are known as its medians.

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of 27:1.

Show that the line joining any vertex of a parallelogram to the mid - point of an opposite side divides the opposite diagonal in the ratio 2 : 1.

Find the ratio of the volume of tetrahedron with that of the tetrahedron formed by the centroids of its faces. Given Volume of tetrahedron =1/3 times area of base triangle times height of vertex.

Line segments joining the vertices to the mid- points of the opposite sides to a triangle are known as medians (b) altitudes (c) heights (d) angle bisectors