Read "An Eye for Similarity Transformations", pp. 109 to mid 116. We will abbreviate this as EST.

Construct (with Sketchpad) the following figures and write the discussions asked for.

Draw two parallel segments AB and CD of unequal length. Construct the two centers of similitude for the two segments as in Figures 10 and 7 of EST. Then answer the following questions.

1. Write a clear proof, using the idea of dilations, that midpoints of the two segments are collinear with the two center of similitude.
2. Interpret (a) as a statement about trapezoids that we encountered as an earlier problem

Draw two circles with different radii in Sketchpad. Construct the two centers of similitude, E and I.

1. Move the circles so that each is exterior to the other. Construct all common tangents. Print out the figure.
2. Move the circles so that they are tangent to each other. Describe what happens to E and I and what happens to the common tangents.
3. Move the circles so that they intersect in two points. Describe what happens to E and I and what happens to the common tangents.
4. Move the circles so one is inside the other. Describe what happens to E and I and what happens to the common tangents.
5. If O1 and O2 are the centers of the circles, prove that EO1/EO2 = - IO1/IO2.

With straightedge and compass or with Sketchpad, draw two intersecting lines and a point P as in Example 2 of EST. Then construct the two circles through P which are tangent to both the lines.