Concept Byte: Parallel Lines and Related Angles

Use With Lesson 3-2

TECHNOLOGY

Activity

Use geometry software to construct two parallel lines. Check that the lines remain parallel as you manipulate them. Construct a point on each line. Then construct the transversal through these two points.

1. Measure each of the eight angles formed by the parallel lines and the transversal. Record the measurements.
2. Manipulate the lines. Record the new measurements.
3. When a transversal intersects parallel lines, what are the relationships among the angle pairs formed? Make as many conjectures as possible.

Exercises

4. Construct three or more parallel lines. Then construct a line that intersects all the parallel lines.
   1. What relationships can you find among the angles formed?
   2. How many different angle measures are there?
5. Construct two parallel lines and a transversal perpendicular to one of the parallel lines. What angle does the transversal form with the second line?
6. Construct two lines and a transversal, making sure that the two lines are not parallel. Locate a pair of alternate interior angles. Manipulate the lines so that these angles have the same measure.
   1. Make a conjecture about the relationship between the two lines.
   2. How is this conjecture different from the conjecture(s) you made in the Activity?
7. Again, construct two lines and a transversal, making sure that the two lines are not parallel. Locate a pair of same-side interior angles. Manipulate the lines so that these angles are supplementary.
   1. Make a conjecture about the relationship between the two lines.
   2. How is this conjecture different from the conjecture(s) you made in the Activity?
8. Construct perpendicular lines a and b. At a point that is not the intersection of a and b, construct line c perpendicular to line a. Make a conjecture about lines b and c.

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