EMAT 6700
by Brad Simmons
Constructing Similar Polygons
Use geometer's sketchpad to construct similar polygons.
In order to construct a polygon similar to an existing polygon, follow the four step process listed below. The new similar polygon will have sides twice as long as the sides of the original existing polygon.
Step 1 Choose any point either inside or outside the polygon and label it point O.
Step 2 Draw rays from point O through each vertex of the polygon.
Step 3 For vertex V, construct a segment OV. Select point V and segment OV. Construct circle by center and radius. Construct the intersection of circle V and ray OV. Label this intersection point V'. Segment OV and segment VV' are congruent. Thus, the length of segment OV' is twice as long as the length of segment OV.
Step 4 Repeat Step 3 for each vertex. Connect point V', W', X', and Y' to form the new polygon.
Construct a polygon similar to polygon VWXY with the sides of V'W'X'Y' twice as long as the original polygon VWXY. Construct the polygon by locating point O outside the original polygon.
1. Locate point O outside the polygon.
3. For vertex V, construct a segment OV. Select point V and segment OV. Construct circle by center and radius. Construct the intersection of circle V and ray OV. Label this intersection point V'.
4. Select circle V. Hide the circle. Repeat Step 3 for each vertex.
5. Connect point V', W', X', and Y' to form the new polygon. Hide all the construction lines.
Please click here for a geometer's sketchpad sketch of the figure shown above.
Construct a polygon similar to polygon VWXY with the sides of V'W'X'Y' twice as long as the original polygon VWXY. Construct the polygon by locating point O inside the original polygon.
Notice that the placement of point O does not affect the size or shape of V'W'X'Y', only its location.
Please click here for a geometer's sketchpad sketch of the figure shown above.
Construct a similar polygon with sides twice as long as those of the given polygon.
Please click here for a geometer's sketchpad sketch of the figure shown above.
Construct a similar polygon with sides 1.5 times as long as those of the given polygon.
(Explain the modification that must be made to the steps used in the previous construction examples)
Please click here for a geometer's sketchpad sketch of the figure shown above.