Group Activity Cards

Geometry Use groups of 2. Materials: Compass, straightedge, metric rulers

A Certain Similarity

Trace onto tracing paper the quadrilateral shown below. Draw a point anywhere outside the figure and label it P. Draw lines from point P through each vertex of the figure. Open a compass to the length of segment PA. Then place the point of the compass on point A and, using the same compass opening, draw an arc intersecting the line through P and A. (Extend the line if necessary.) Repeat the above for each of the other three vertexes.

Draw line segments connecting the four points of intersection. The resulting figure should be similar to, but twice as large as, the original figure. Write and solve proportions to determine if the two figures are actually similar.