Geometry Investigation Magnets Solution
Let’s experiment with a general right triangle. The sides of the triangle can
be a, b, and c—where c is the longest side. Below are two large squares,
each of which has side length a+b.
Can you arrange the gray triangles inside the squares so that in one box you
are left with a square with side length “c” and in the other box you are left
with two squares—one with side length “a” and one with side length “b”?
Make sure to use four triangles in each box.
What do you know about the white area left in each box? What does this tell
you about how the pattern you found might work for a right triangle with
sides a, b, and c?
A general r
The gray triangles are all congruent,
so the gray area we’ve created in each
box must be equal. This means that
the leftover area in white must also
For a right triangle with sides a,
b, and c, the square of c is equal
to the squares of a and b added
e is c
sides of length
ea of this
square is b
e is a
128 Chapter 3