Drag these points around. This figure has no constraints (Givens). What things appear to be congruent? Angles? Segments? Triangle? What things can you conclude with certainty? How do you know?
Let's add the following constraint: G is the midpoint of F and H. Now drag the points around. What things appear to be congruent? Angles? Segments? Triangle? What things can you conclude with certainty? How do you know?
Let's add one more constraint: Segment EF is congruent to segment EH. Now drag the points around. What things appear to be congruent? Angles? Segments? Triangle? What things can you conclude with certainty? How do you know?