Four Triangles Equal in Area

The Activity problem

What is the relationship between the areas of the four triangles obtained by joining the midpoints of the sides of a triangle?















Conjecture

The areas of the four triangles obtained by joining the midpoints of the sides of a triangle are equal.
Please enable Java for an interactive construction (with Cinderella).
Drag free points A, B, or C to alter the triangle ABC several times and visually observe the area of the four triangles in each time.