Question

The figure below can be used to prove the Pythagorean Theorem. Use the drop-down menusto complete the proof.aababClick the arrows to choose an answer from each menu.The expression Choose... represents the area of the figure as the sum of the area of theshaded triangles and the area of the white square.The equivalent expressions Choose...use the length of the figure torepresent the area.Setting two of these area expressions equal to each other and subtracting Choose...from both sides of the equation results in the Pythagorean Theorem, a? + b2 = c?.

Answer 1

2ab + c²

(a+b)² and a² + 2ab + b²

2ab

1) Examining that picture, we can state the following about that:

The shaded triangles area:

`(1)/(2)ab\text{ +}(1)/(2)ab+(1)/(2)ab+(1)/(2)ab=2ab`

Note that the area of the triangle is 1/2 the product of the base by its height.

The area of that white inner square is given by c² since the Area of a square is equal to the side length raised to the 2nd powe.

2) Then

The expression 2ab + c² represents the area...

The equivalent expressions (a+b)² and a² + 2ab + b² use the length of the figure (a square) raised to the 2nd power. As explained above.

For the last statement let's calculate it:

2ab + c² = (a+b)²

a² +2ab + b² = 2ab +c² Subtracting 2ab

a² +b² = c²

3) Hence, the answers are:

2ab + c²

(a+b)² and a² + 2ab + b²

2ab