Parallel lines are two lines in the same plane that never intersect. Another way to think about parallel lines is that they are "everywhere equidistant." No matter where you measure, the perpendicular distance between two parallel lines is constant. With dynamic geometry software, you can draw two lines that look parallel, but you can't be sure that they are parallel unless you construct them to be parallel. Note 2
Follow these steps to construct two parallel lines:
Using the Line Tool in Geometer's Sketchpad, draw a line.
Pull down the Construct menu in Sketchpad. You'll notice that the "Parallel Line" is gray -- therefore, not an option to you. This is Sketchpad's way of telling you that you don't have the correct objects selected or you don't have enough objects selected. What else do you need to construct a line parallel to your original line?
Continue your construction and record the steps you used to construct two parallel lines.
Draw a transversal through your parallel lines. (A transversal is a line that passes through two parallel lines.)
Measure each of the angles formed.
Change the orientation of the transversal by dragging one of the defining points. Keep a record of what changes and what stays the same.
To measure an angle, select three points in the order of the angle. You may need to construct additional points on your lines before you can measure the angles. Close Tip
When a pair of parallel lines is cut by a transversal, several special pairs of angles are formed.
ABD and EFB are corresponding angles.
ABF and GFB are alternate interior angles.
ABD and CBF are vertical angles.
ABD and CBD form a linear pair.
Name another pair of corresponding angles, another pair of alternate interior angles, another pair of vertical angles, and another linear pair.
Using this new terminology, summarize the relationships you discovered in Problem B2.