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To construct a square equivalent to the sum of two given squares. |
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To construct a square equivalent to the sum of two given squares. |
| Given: Squares S (ABCD) and S' (EFGH), with sides AD and EH respectively. |
| Required: To construct a square, S", equivalent to the sum of squares S and S'. |
| Procedure: |
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 Use
the square command under the sample tools menu of Custom Tools and
construct two squares S (ABCD) and S' (EFGH). |
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Use the straightedge tool and lay off a segment MP. |
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Use the perpendicular command under the construct
menu and construct a perpendicular at M. |
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Use the circle by center + radius command under the construct menu and
construct a circle with center at M and radius congruent to segment AD. Label the intersection of MP and this circle N. |
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Use the circle by center + radius command under the
construct menu and construct a circle with center at M and radius
congruent to segment EH. Label the intersection of this circle and the
perpendicular O. |
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Use the segment command under the construct menu and construct segment
ON. This is the length of a side of the required square. |
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Use the straightedge tool and lay off a segment LQ. |
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Use the perpendicular command under the construct
menu and construct a perpendicular at L. |
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Use the circle by center + radius command and construct a circle with
center at L and radius congruent to segment ON. Label the
intersection of LQ and this circle I, the intersection of the
perpendicular at L and this circle K. |
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Use the circle by center + radius command and construct a circle with
center at K and radius congruent to segment ON, and another circle with
center at I and radius congruent to segment ON. Label the
intersection of these two circles J. |
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Quadrilateral S" (IJKL) is the required square. |
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You may choose to construct the interiors of all three squares and then calculate the areas to confirm the sketch. |
| Proof: |
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(MN)^2 + (MO)^2 = (ON)^2 (The square of the hypotenuse of a right
triangle is equal to the sum of the squares of the legs. |
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S + S' =
S"
(Substitution) |
| Sketch: Drag either point A or E and check to see if the areas continue to add up. |
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This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use. square equal to sum of two squares |
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