A parallelogram is a quadrilateral with two pairs of parallel sides. We will investigate some of the properties of parallelograms in the following exercise.
1. Draw a horizontal line. Select the line and the points on it and copy it (apple-C), then paste the copy below the original drawing (apple-V). Label all the points in the figure.
2. Connect the two points on the left via a line segment. Similarly connect the two points on the right with a line segment.
3. Copying the figure leaves us with double labels everywhere. This is a bit difficult to work with, so we'll change it. Select the labelling toolbox. Go to the line on the bottom. If you get near the label of the point, you will see an "a" appear in the labelling hand. When this happens, double click. You can now change the label. Change the labels so that they read A,B,C,D when reading them clockwise (starting at the top left).
4. You should now have a quadrilateral ABCD. Measure the length and the slope of AB and CD. Measure the length and the slope of AD and BC. What do you notice?
5. Select the top line and move it up/down and left/right. Describe what happens. Are all the quadrilaterals you get this way parallelograms? How do you know?
6. Measure angles ABC and CDA. Also measure angles DAB and BCD. What do you notice? What happens when you move one of the lines up/down and left/right?
7. Can you think of another way to use GSP to draw parallelograms? Describe your methods. How do you know they are parallelograms?