The 1939 movie The Wizard of Oz

Full Answer Section

    where:

• a and b are the lengths of the two legs of the triangle
• c is the length of the hypotenuse

The Scarecrow's statement contains several errors:

1. Incorrect Terminology: An isosceles triangle is a triangle with two sides of equal length. The Pythagorean Theorem applies to all right-angled triangles, not just isosceles ones.
2. Misunderstanding of Square Roots: The Scarecrow incorrectly states that the sum of the square roots of two sides equals the square root of the remaining side. The correct relationship involves the squares of the sides, not their square roots.
3. Confusing Sides: The Scarecrow seems to be suggesting that the sum of any two sides equals the remaining side. This is not true in general for any triangle, let alone a right-angled triangle.
4. Lack of Right Angle: The Pythagorean Theorem specifically applies to right-angled triangles. The Scarecrow's statement does not mention the requirement for a right angle.

In conclusion, while the Scarecrow's enthusiasm for learning is admirable, his understanding of the Pythagorean Theorem is significantly flawed. The correct statement is that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.    

Sample Answer

   

The Scarecrow's statement is incorrect. While he displays a commendable enthusiasm for learning, his understanding of the Pythagorean Theorem is flawed.

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Mathematically, it is expressed as