Prove that the three triangles are congruent.
Write down the formula for calculating the area of rectangles that are displayed by numbers.
Move the point D up. Then move down points E and F. Did the rectangular areas change?
Now write a new formula for the area of resulting squares.
Write the equality between the sum of these rectangular areas at the beginning and at the end.
Move points A, B and C at some new positions. Then repeat the previous procedure. What do you conclude?