AND PLEASE SHOW YOUR WORK :))

  A: c^2

  B: (1/2)ab

  C: a^2 +b^2 = c^2 . . . Pythagorean theorem

Step-by-step explanation:

A. The area of the square with side length c is the product of the side lengths:

  small square area = c·c = c^2

B. The area of a triangle is half the product of its base and height:

  triangle area = (1/2)ab

C. Doing what the instructions say, we have ...

  a^2 +2ab +b^2 = 4(1/2)ab +c^2

  a^2 +b^2 = c^2 . . . . . . . . . . . . . . . . .  subtract 2ab from both sides

This is a statement of the Pythagorean theorem.

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: