In the picture below, the top vertex of a triangle is joined to the midpont of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices:
Prove that the areas of all three triangles in the picture on the are equal to a third of the area of the whole triangle.

In the picture below, the top vertex of a triangle is joined to the midpoint of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices. Prove that the areas of all three triangles in the picture on the right are equal to a third of the area of the whole triangle

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.

In the picture below, two vertices of a parallelogram are joined to the mid points of two sides. Prove that these lines divides the diagonal in the picture into three equal parts. .

In the picture below, two lines are drawn from the top vertex of a triangle to the bottom side: Prove that the ratio in which these lines divide the length of the bottom side is equal to the ratio of the area of the three smaller triangles in the picture.

In the figure,AD is the line joining a vertex to the mid point of the opposite side. G is a point on AD which divides AD in the ratio 2:1 as AG:GD=2:1 Name the triangle having equal area in the picture

In the figure,AD is the line joining a vertex to the mid point of the opposite side. G is a point on AD which divides AD in the ratio 2:1 as AG:GD=2:1 What is the area of triangle BGC.

In the figure,AD is the line joining a vertex to the mid point of the opposite side. G is a point on AD which divides AD in the ratio 2:1 as AG:GD=2:1 The area of /_\BGA is 24 cm^2 .What is the area of /_\BGD ?

In this picture the horizontal lines at the top and bottom are parallel. Prove that the yellow and red triangles are of the same area.

In this picture the horizontal lines at the top and bottom are parallel. Prove that the yellow and red triangles are of the same area.