Geometry I 5.7 Problem #4

Suppose ABCD is a parallelogram, P is on AC and lines through P parallel to the sides of the parallelogram intersect the sides at W, X, Y, and Z as indicated. Move points A, B, C, and P around. Observe the ratios below the parallelogram.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

1. Is XY ∥ BD? Explain why.

2. In general, why type of quadrilateral is WXYZ? Explain.

3. Using the buttons given, determine where P needs to be in order for WXYZ to be a parallelogram? (Hint: Use angle measurements and segment lengths)

4. Can points A, B, C, and P be moved so that WXYZ is a rectangle? A square? If so, what would have to be true about ABCD and the point P?

Mindy Burcham, Created with GeoGebra