Four Triangles Equal in Perimeter

Proposed Problem 1 What is the relationship between the perimeters of the four triangles obtained by joining the midpoints of the sides of a triangle? Conjecture The preimeter of the four triangles obtained by joining the midpoints of the sides of a triangle is equal.	Please enable Java for an interactive construction (with Cinderella).
	Drag free points A, B, or C to realize that the preimeter of the four triangles obtained by joining the midpoints of the sides of a triangle is equal.