Construct a pair of inscribed triangles. First, explore the given figure. Note the dependencies in the figure. Then construct your own pair of inscribed triangles that behaves the same way. Triangle DEF is called “inscribed” in triangle ABC if its vertices D, E and F are on the sides of triangle ABC.
If you solved this, did you construct the lengths of the sides of the outer triangle to be directly dependent upon each other? Did you construct the lengths of the sides of the inner triangle to be directly dependent upon each other? Do you think that the triangles are equilateral? How do you know?