I failed math when I corrected my math teacher. She said pie are square, I reminded her that pie are round.
I hate to play the devil’s advocate, ( Ok, I revel in the role ) but the instructor fails to mention if it is a “right” triangle or not. If it is an isosceles triangle or an equilateral triangle, the theorem is useless!?! Therefore everyone in the room is correct to question his statement…..
If the square on the hypotenuse is equal to the sum of the squares on the other two sides of a right angled isosceles triangle then how many times does the triangle fit into the larger figure comprising the triangle and the squares?
Interesting question. Sadly though, I just did the values for the Pythagorean triples 3.4.5 and 5.12.13 and perhaps as you may expect they came out differently, ( Nine and two thirds, and twelve and four fifteenths, including the area of the original triangle. ) so it would seen that there is no constant value.
Isosceles.
@waitingforgodo Every Isosceles triangle is made up of two identical right angled triangles.
Every isosceles triangle has two sides each to x and a hypotenuse equal to the x times the square root of 2.
The ratio of the sides is 1: 1: root 2
The ratio of the square on the hypotenuse equals 2 square units and the ratio of the squares on the other twp sides equal 1 square unit each.
The area of the triangle has an equivalent ratio of 1/2