Transcript Pythagorean Theorem

Pythagorean Theorem
A quick visual proof
Consider the following square
a
b
b
c
c
a
c2
a
c
b
c b
a
 There are four
congruent yellow right
triangles with sides a,
b and hypotenuse c.
 Note that there are
four triangles and one
square
 The square has side
length of c so its area
is c2
 The sides of the
square have a length
of a+b
Now, consider this square
a
b
c
b2
b
a
a2
a
c
b
b
a
 Note that this square
still has side lengths of
a+b and still has four
yellow triangles with
sides a and b and
hypotenuse c.
 This time instead of
one square with area
c2, there are two
squares: one with area
a2 and one with area
b2.
To conclude
 Both squares have the same side lengths
therefore, they have the same area.
 Both squares have four congruent triangles
with sides a and b and hypotenuse c. So,
each region of the square containing these
triangles must have the same area.
 If I subtract the area of the region
containing the triangles from the area of
the entire square, the two regions that are
left must have an equal area.
 So, c2 = a2 + b2
Proof without words