4. Area of Whole Square :
A = (a+b)(a+b)
Area of the smaller (tilted) square :
A= c²
Area of four triangles :
A=4(1/2 ab) = 2ab
The area of the large square is equal to the area of the tilted square and
the four triangles.
(a+b)(a+b) = c² + 2ab
a² + 2ab +b² = c² + 2ab Expanding (a+b)(a+b)
a² + b² = c² Subtraction Property of Equality
Proof:
a² + b² = c²

5. The Pythagorean theorem
can be illustrated visually in
several ways. One such
illustration is shown by the
figure on the right. Square A
is divided into four regions
by two dashed lines that pass
through its center. One
dashed line is parallel to the
left edge of square C, and the
other dashed line is parallel
to the lower edge of square
C. If these four regions and
square B are traced and cut
out, they can be arranged to
cover square C. Try it!

6. Starting Points for Investigations
1. Draw a right triangle with legs of length 1 inch and 2
inches and a square on each of its sides. (Right angles
can be drawn by using the corner of a file card.)
Subdivide the larger of the squares on the legs into four
regions as described in the figure on the previous slide.
Show how these four regions and the square on the other
leg can be arranged to exactly cover the square on the
hypotenuse.
2. Suppose the smaller of the squares on the legs of a
right triangle is subdivided into four regions as described
above. Can these regions and the square on the other leg
be arranged to cover the square on the hypotenuse?