Demonstrating the
Pythagorean Theorem
You know
what a right triangle is. Right?
It has
one right angle.
(Could it
have more than one? That is worth thinking about for a minute.)
A right
triangle always has one side that is longest.
The
longest side is always across from the right angle.
It has a
name: hypotenuse.
The other
two sides will always be shorter than the hypotenuse.
They
always come together to “create” the right angle.
A long
time ago, a mathematician named Pythagoras figured out that there is always a
relationship between the lengths of the three sides of a right
triangle. We could measure the lengths of the two short sides and
call those lengths a and b. We could
measure the length of the hypotenuse and call it c.
Here is the relationship:
a2 + b2 =
c2
Pythagoras liked to picture things
geometrically. So the way he really thought about this formula was
like this: If I take the right triangle, and if I draw a square on
each of the three sides, then the areas of the two smaller squares will always
add up to equal the area of the big square.
Demonstrate the Pythagorean Theorem using the square and the triangles you were given.
If it helps to see another set of geometric figures, here is another set. These are slightly different than the ones above, but they work just as well to demonstrate the theorem. Enjoy!
