Wingeom: Dilation & Similarity
Getting Started
Double click on the Wingeom icon. Select Window / 2 dim; inflate frame. Put
the mouse in the Btns / Segments mode. Plant points A, B, C and D on the screen. If you
do not see the little circles that represent points, do Edit, labels, offset. Connect A to B,
B to A, and C to A. Plant point D, this is the point of dilation.
Constructing Rays
Select Line on the command bar. In the pop-up frame select Rays. In the new
pop-up frame type DA, DB, DC.
Transformation Dilation
Select Transf on the command bar. In the pop-up frame select dilate. Fill in the
new pop-up frame with this information: vertices ABC, center D, angle 0, dilation factor
1.5, followed by ok.
Adjust the Vertices and Labels
To change the shape of the diagram, the only vertices that you can move by Btns
/drag vertices are those in the original set A, B, C, and D. Try moving any of the others.
However, anyone of the labels can be adjusted using Btns / text.
Measurements
Select Meas from the command bar. Find the measure of each of these: DA’, DA,
DA’/DA; this quantity equals the dilation factor 1.5.
Also find the measure A’B’/AB; since the value is equal to 1.5, this suggests that
the ratio of two corresponding sides is equal to the dilation factor.
Finally, find the ratio of the areas, A’B’C’/ABC. The value 2.25 is equal to the
dilation factor squared, check by typing 1.5^2 in the measure space.
Note, too, that two triangles are similar, since the corresponding sides are in the
same proportion. Of course, the corresponding angles of the two triangles will be equal.
Position the measures on the screen by using Btns / text. See the diagram above.
Writing Text on the Screen
With the mouse in the Btns/text mode, right click on the screen where you want
the text to appear. Type Title: Dilation & Similarity, then click ok. Repeat this
procedure for your Name, Teacher, Period. Using the left mouse button and cursor adjust
the text.
Printing the Document
Do File / Format, change the upper number to 25 / ok. The horizontal and vertical
offsets should be 2.54. We want the document to print in the landscape mode. The
following set of commands will work on some computers; others might have a different
set of commands. Do File / Print / Propeties / Basics (layout) / Landscape / ok. Print the
document.