1. lnyg:tigotig,
There is a special relationship among the areas of squares
constructed on the three sides of a right triangle.
The dissection puzzle in this investigation is
intended to get you thinking about this special
relationship. On a full sheet of paper, perform
G
Steps 1-6. Note that the arcs and the segment
'B-r -,
extensionsnecessary completeSteps I and
to
2 are not indicated in the figure-
Construct a scaleneright triangle in the middle of
Siep I
your paper (hypotenusedown). Label it so that the
hlryotenuse is AB and the longer leg is BC.
Construct a square on each side of the triangle. Label
Step 2
the square on the longer leg BCDE Label the square
on the shorter leg AGFC.Label the square on the
hlryotenuse ABIH.
point O'
Locate the center af BCDE(intersectionof the two diagonals).Label the
Step 3
Through point q construct line i perpendicular to the hypotenuse'
4
Step
Through point O, construct line k perpendicular to line j. Line k is parallel to the
5
Step
hypotenuse.Lines j and k divide BCDEinto four parts.
Arrange them to exactly cover
and the four parts of square BCDE.
Cut out square AGFC
6
Step
square ABIH on the hYPotenuse.
If you are successful,then you have demonstrated that the area of the square on the
hypotenuse is equal to the sum of the areasof the squareson the two legs of your
triangle. Compareyour results with the results of others near you. If the lengths of the
two legs of a right tiangle are a and b, then the areasof the squareson the Iegs are a2
and b2.If the length of the hytrlotenuse c, then the area of the square on the
is
your observationsas your next coniecture'
hypotenuse is c2. State
geomettyan inductive (pp.a75-522).
approach.
Serra,M. [1997).Discovering
Emeryville,CA:Key CurriculumPress.