**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.