By moving point G, how many triangles is it possible to draw, keeping the measure of just one angle constant (in this case, m∠FDE)? In how many instances are all three angle measures of ∆DEF equal to those of the original triangle, ∆ABC?

Step-by-step explanation:

Keeping,  one angle FDE, many triangles are possible since length of no segment is fixed and only one angle is fixed.

At many instances, triangle ABC and DEF have same angle measurements. Referring to the image attached here.

As point G moved on the ray EF, many triangles with same angle measurements as of ABC can be formed.