Algebra Equation

Question

In the 1939 Movie The Wizard of Oz, upon being presented with a Th.D (Doctor of Thinkology), the Scarecrow proudly exclaims, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side@

Did the Scarecrow get the Pythagorean Theorem right? In particular, point out and describe the errors in the Scarecrow’s statement.

Answer 1

No, He did not get the theorem right.

First, the Pythagorean theorem applies to right triangles, not isosceles (those some isosceles triangles are also right triangles).

Let's look at the Pythagorean theorem: A² + B² = C² , where C is the hypotenuse and A and B are the shorter two sides.

First, we are looking at the square of the sides, not the square root.

Second, it is the sum of the squares of the shorter two sides, not any two sides.

So to put it together: the Pythagorean Theorem says that the sum of the squares of the shorter two sides of a right triangle is equal to the square of the hypotenuse (the remaining side).