Question to Explore: What if a triangle is not a right triangle?  Will the Pythagorean Theorem hold for acute or obtuse triangles?
This question can lead to development of a more useful "Law" about the relationship between the three sides of any triangle.

Download the Mystery Law GSP sketch.

For the case in which the triangle is acute, the sum of the areas on the legs is greater than the area of the square of the hypotenuse.   If the triangle is obtuse, the sum of the areas on the legs is less than the area of the square of the hypotenuse.

Use the sketch and your algebra and trigonmetry skills to establish a general "Law" for a relationship between the three sides of any given triangle.