Area Relationship

Proposed Problem 2

What is the relationship between the area of each  of the four triangles obtained by joining the midpoints of the sides of a triangle and the area of the original triangle?






Conjecture


Surface area of each small triangle = ¼ Surface area of the original triangle.
Please enable Java for an interactive construction (with Cinderella).
Drag free points A, B, or C and observe triangles surface areas to realize that the surface area of each small triangle = ¼ Surface area of the original triangle.