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To construct a polygon similar to a given polygon and with a given ratio of similitude. |
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To construct a polygon similar to a given polygon and with a given ratio of similitude. |
| Given: Polygon P and segment A'B' corresponding to segment AB, and AB:A'B' the ratio of similitude. |
| Required: To construct a polygon similar to P with AB and A'B' corresponding sides. |
| Procedure: |
The construction will be completed with a given pentagon, ABCDE.
The method can be extended to any polygon. |
Use the segment tool under the construct menu and construct segments for
all possible diagonals from point A: AC, AD. Angles formed
are  BAC,
CAD,
and DAE. |
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At A' construct BAC
=B'A'X,
CAD =XA'Y,
and DAE
=YA'Z
(help) |
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At B', construct A'B'R
= ABC
(help) |
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Label the intersection of ray A'X with B'R, point
C'. |
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AT C', construct A'C'S
= ACD
(help) |
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Label the intersection of ray A'Y with C'S, point D'. |
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AT D', construct A'D'T
= ADE
(help) |
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Label the intersection of ray A'Z with D'T, point E'. |
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Polygon P', A'B'C'D'E', is the required
polygon. |
| Proof: |
The  s
of P are similar respectively to the s
of P' and arranged in the same order. ( 2 s
of one = 2 s
of the other) |
P' 
P (If two polygons are composed of the dame number of triangles,
similar to each and similarly placed, the polygons are similar) |
| Sketch: |
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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. construct similar polygon |
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