Transcript Document 7490523

Picture This!
Pythagorean Theorem
c
a
b
step by step
start with a
right triangle
label the sides
c
a
b
construct a square
on each side
c
a
b
find the center of the
square on a by drawing
its diagonals
c
a
b
Then copy side c
c
a
b
and slide it
over−parallel to side c
c
a
b
to the center of
the square on a
Draw the perpendicular
bisector
c
a
b
The 2 perpendicular bisectors
at the center divide
the square into
c
a
b
4 equal parts
The length of each arm
radiating out from the center
c
2
c
2
c
2
c
2
c
is equal to half of side c
Sliding side c along the base
to the center of the square
c
also makes a parallelogram
So side b of the triangle
plus the shortest side
of the quadrilateral
b
c
b
is equal to the long side of
the quadrilateral.
slide the 4 quadrilaterals
over to the big square
c
a
b
The outsides fit because each
one is half of side c.
c
a
b
The insides fit because each
one equals side b plus the
short side
c
a
b
The square on b fills the
space in the middle of
the square on c
c
a
b
so we’re done!
We had to cut up the square
on side a to do it, but
we proved that
c
a
for
right
triangles...
b
the sum of the squares on
the legs
c
a
b
is equal to the square on
the hypotenuse
c
a
b
a2 + b2 = c2
c
a
b