Explaining the Converse of the Pythagorean Theorem The converse of the Pythagorean Theorem states that if the three sides of a triangle work for the equation a2 + b2 = c2, then the triangle is a right triangle. To prove this, you can use what’s called a proof by contradiction. That is, you can prove something is true because it cannot be false.

Start by assuming a triangle is not a right triangle and the sides work for the equation a2 + b2 = c2. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.

Now, create a right triangle with legs a and b. Call the hypotenuse n. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.
DIAGRAM 1 AND 2 ATTACHED
Part A
Since triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle?

Part B
Since the equations for both triangles have a2 + b2, you can think of the two equations for c2 and n2 as a system of equations. Substitute what a2 + b2 equals in the first equation for a2 + b2 in the second equation. After you substitute, what equation do you get?

Part C
Now, take the square root of both sides of the equation from part B and write the resulting equation.

Part D
Is there any way for this equation to be true? How?

Part E
What does this show about the relationship between the two triangles?

Part F
Does this mean that triangle 1 is a right triangle? Why or why not?