Question

Can you use the converse of the Pythagorean theorem to determine if a triangle is a right triangle?

Answer 1

It's important to know that the converse of the Pythagorean Theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Let's apply the converse to the given triangle.

`\begin{gathered} 6^2=4^2+5^2 \\ 36=16+25 \\ 36=41 \end{gathered}`

As you can observe, this result is false because 36 is not equal to 36.

Therefore, by the converse of the Pythagorean Theorem, the triangle is not a right triangle.