Prove that the centroid of any triangle is the same as the centroid of the triangle formed by joining the middle points of its sides

Centroid of a Triangle

Centroid of triangle

prove that the area of a triangle is four times the area of the triangle formed by joining the mid-points of its sides.

Find the centroid of the triangle ABC whose vertices are A (9, 2), B (1, 10) and C (-7, -6) . Find the coordinates of the middle points of its sides and hence find the centroid of the triangle formed by joining these middle points. Do the two triangles have same centroid?

If Delta_(1) is the area of the triangle formed by the centroid and two vertices of a triangle Delta_(2) is the area of the triangle formed by the mid- point of the sides of the same triangle, then Delta_(1):Delta_(2) =

The middle points of the sides of a triangle are joined forming a second triangle. Again a third triangle is formed by joining the middle points of this second triangle and this process is repeated infinitely. If the perimeter and area of the outer triangle are P and A respectively, what will be the sum of perimeters of triangles thus formed?

The semiperimeter of a triangle is S and its centroid is G. What is the distance between G and centroid of the triangle formed by mid points of the sides of the given triangle ?

Fill in the blanks to make the following statements correct The triangle formed by joining the mid-points of the sides of an isosceles triangle is .... The triangle formed by joining the mid-points of the sides of a right triangle is .......... The figure formed by joining the mid-points of consecutive sides of a quadrilateral is ....