EMERGENCY The figure below can be used to prove the Pythagorean Theorem. Use the drop down menus to complete the proof. Click the arrows to choose an answer from each menu.

Follow along and see the highlighted bold text for the drop-down answers.

Our first option is asking for the expression which is the sum of the area of:

a. the shaded triangles

and b. the white square

The area of the shaded triangles can be found by using the formula for the area of a triangle.

A = (base * height) / 2

On these triangles, the base is b and the height is a.

Since there are 4 triangles, we'll multiply this expression by 4.

The area of the white square can be found using the formula for the area of a square.

A = side * side = side^2

The side of our square is c.

The sum of these areas is, thus:

(our first expression)

The area of the larger square, the entire figure, can be found using the formula for the area of a square that we used above. The side of this square is (a + b):

(our 2nd expression)

We also choose to expand the parenthesis using the appropriate rule to get the above expression.

Now, following the proof, we set both of these expressions equal to each other and subtract something. Let's put these 2 expressions (the sum of the triangle and the white square, and the larger square) equal to each other:

Since 2ba = 2ab, we can subtract this from both sides. (we subtract 2ab)

Flipping this equation, we get the Pythagorean Theorem: