A Preview of Lesson 3-2
Angles and Parallel Lines
You can use The Geometer’s Sketchpad to investigate the measures of angles
formed by two parallel lines and a transversal.
Draw parallel lines.
Construct a transversal.
Place two points A and B on the screen.
Place point E on AB and point F on CD.
Construct a line through the points.
Construct EF as a transversal through AB
Place point C so that it does not lie on AB.
Place points G and H on EF, as shown.
Construct a line through C parallel to AB.
Place point D on this line.
Measure each angle.
List pairs of angles by the special names you learned in Lesson 3-1.
Which pairs of angles listed in Exercise 1 have the same measure?
What is the relationship between consecutive interior angles?
Make a Conjecture
Make a conjecture about the following pairs of angles formed by two parallel lines
and a transversal. Write your conjecture in if-then form.
alternate interior angles
alternate exterior angles
consecutive interior angles
Rotate the transversal. Are the angles with equal measures in the same relative
location as the angles with equal measures in your original drawing?
Test your conjectures by rotating the transversal and analyzing the angles.
Rotate the transversal so that the measure of any of the angles is 90.
What do you notice about the measures of the other angles?
Make a conjecture about a transversal that is perpendicular to one of two
132 Chapter 3 Parallel and Perpendicular Lines