|
|
To construct a square equivalent to the difference of two given squares. |
|
|
To construct a square equivalent to the difference of two given squares. |
| Given: Squares S (ABCD) and S' (EFGH) with sides AD and EH respectively. Let S' be the larger square. |
| Required: To construct a square S" equivalent to the difference of squares S' and S. |
| Procedure: |
|
|
Use the square command under the sample tools menu of Custom Tools and
construct two squares S (ABCD) and S' (EFGH) |
|
Use the straightedge tool and lay off a segment MP. |
|
Use the perpendicular command under the construct
menu and construct a perpendicular at M. |
|
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. |
|
Use the circle by center + radius command under the
construct menu and construct a circle with center at N and radius
congruent to EH. Label the intersection of the perpendicular and
this circle O. |
|
Use the segment command under the construct menu and construct a segment
MO. |
|
Use the straightedge tool and lay off a segment LQ. |
|
Use the perpendicular command under the construct
menu and construct a perpendicular at L. |
|
Use the circle by center + radius command under the construct menu and
construct a circle with center at L and radius congruent to segment
MO. Label the intersection of LQ and this circle I, the
intersection of the perpendicular at L and this circle K. |
|
Use the circle by center + radius command and construct a circle with
center at K and radius congruent to segment MO, and another circle with
center at I and radius congruent to MO. Label the intersection of
these two circles J. |
|
Quadrilateral S" (IJKL) is the required square. |
|
You may choose to construct the interiors of all three squares and then
calculate the areas to confirm the sketch. |
| Proof: |
|
(MN)^2 + (MO)^2 = (NO)^2 (The square of the hypotenuse of a right
triangle is equal to the sum of the squares of the legs.) |
|
(MO)^2 = (NO)^2 - (MN)^2
(Subtraction) |
|
S" = S' -
S (Substitution) |
| Sketch: Drag points A or E and see if the calculations hold. |
|
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 difference of two squares |
|
|
