How do you do #2?
the triangle below is a right triangle. show that this triangle satisfies the pythagorean theorem

Explanation:

How: Show the sum of the squares of the leg lengths is the square of the hypotenuse length.

The square of the length of each leg can likewise be found using the Pythagorean theorem. The upper left leg is the hypotenuse of a right triangle with legs of 1 and 2 units. It square will be ...

  1² + 2² = 5

Likewise, the upper right leg is also the hypotenuse of a 1×2 right triangle. Its square is also 5.

The hypotenuse of the triangle shown is the hypotenuse of a 1×3 right triangle connecting the grid dots. Hence its square will be ...

  1² +3² = 10

The fact that the squares of the legs have a sum equal to the square of the hypotenuse verifies that the triangle shown is a right triangle that satisfies the Pythagorean theorem:

  (upper left leg)² + (upper right leg)² = hypotenuse²

  5 + 5 = 10 . . . . . the theorem is satisfied

a negative exponent is translated as follows:

so, we have