Alternate Exterior Angles

Topic:
Angles

What do we know about the relationship between alternate exterior angles?

Are they always congruent? What are the necessary and sufficient conditions for them to be congruent?

Objectives

Students will be able to:
  • determine the nature of the relationship between alternate exterior angles
  • determine the necessary and sufficient conditions for alternate exterior angles to be congruent
  • articulate why alternate exterior angles must or must not be congruent based on given criteria

Example 1: Lines f and j are parallel.

  1. What do you notice about the alternate exterior angles, highlighted in green, that are created by transversal h?
  2. Drag the red diamond along the dotted line. What happens to the measures of the alternate exterior angles?
  3. Given your observations, make a conjecture about the relationship between alternate exterior angles.

Example 2: Lines f and g are not parallel.

  1. What do you notice about the alternate exterior angles, highlighted in green, that are created by transversal h?
  2. Drag the red diamond along the dotted line. What happens to the measures of the alternate exterior angles?
  3. Compare these observations to those you made in the previous example. How are they the same? How are they different? If necessary, alter your conjecture about the relationship between alternate exterior angles.

Example 3: Lines f and g are not parallel.

Will the alternate exterior angles, highlighted in green, that are created by transversal h be congruent?

Why or why not? Use your refined conjecture and observations as part of your justification.