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Mathematics, 12.04.2021 07:50 tryintopassenioryear

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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 a^2 + b^2 = c^2,
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 in the sides work for the equation a^2 + b^2 = c^2, (here is the diagram of the triangle)

Keep this diagram window open as you work on the task 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 task in a section.

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 a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 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?

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