In the 1939 classic movie The Wizard of Oz, Ray Bolger’s character, the Scarecrow, wants a brain. When the Wizard grants him his “Th.D.” (Doctor of Thinkology), the Scarecrow replies with the following statement.

Scarecrow: The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.

His statement sounds like the formula for the Pythagorean theorem. To see why it is incorrect, work Exercises in order.

Data from in Pythagorean theorem

An isosceles triangle has two sides of equal  length. Draw an isosceles triangle with two sides  of length 9 units and remaining side of length  4 units. Show that this triangle does not satisfy the Scarecrow’s statement.