She is correct. Two different shapes can take up the same amount of space ("area") and have the same number of edges of the same length ("perimeter").
Example: https://i.stack.imgur.com/dVVvg.jpg The red and green shapes are completely different from one another, but have the same area and perimeter.
Two shapes are only "congruent" if you can do a "rigid transformation" of one into the other. Notice how this is connected to your previous lessons. 😉
omg real :DDD