![]() They have, however, studied the idea of 180 degree rotations in a previous lesson where they used this technique to show that a pair of vertical angles made by intersecting lines are congruent. This provides a deeper understanding of the relationship between the angles made by a pair of (not necessarily parallel) lines cut by a transversal.Įxpect informal arguments as students are only beginning to develop a formal understanding of parallel lines and rigid motions. The second question is optional if time allows. The goal of this task is to experiment with rigid motions to help visualize why alternate interior angles (made by a transversal connecting two parallel lines) are congruent. This result will be used in a future lesson to establish that the sum of the angles in a triangle is 180 degrees. Congruent angles in corresponding positions at the two vertices were only true in the first two pictures, which had parallel lines.) "Which angle relationships were true for all three pictures? Which were true for only one or two of the pictures?" (Congruent vertical and supplementary angles around a vertex were always true."What do you notice about the angles at vertex \(B\) compared to the angles at vertex \(E\)?" (They have the same angle measures for angles in the same position relative to the transversal.)."What were some angle relationships you used to find missing measures?" (Vertical angles, supplementary angles)."What were some tools you used to find or confirm angle measures?" (Tracing paper, protractor, transformations).After students point out the matching angles at the two vertices, define the term alternate interior angles and ask a few students to identify some pairs of angles from the activity.Ĭonsider asking some of the following questions: Encourage students to use precise vocabulary, such as supplementary and vertical angles, when describing how they figured out the different angle measurements. Display the images from the Task Statement for all to see one at a time and invite groups to share their responses. The purpose of this discussion is to make sure students noticed relationships between the angles formed when two parallel lines are cut by a transversal and to introduce the term alternate interior angles to students. Monitor for students who use these different strategies and select them to share during the discussion.įor students who finish early, ask them to think of different methods they could use to determine the angles: For example, all of the congruent angles can be shown to be congruent with transformations. ![]() Similarly, to find measures of vertical angles students may use a \(180^\circ\) rotation like they did earlier in this unit when showing that vertical angles are congruent. They might try to translate \(B\) to \(E\) in the third picture and observe that the angles at those two vertices are not congruent. ![]() For example, they may use tracing paper to translate vertex \(B\) to vertex \(E\). To find the measures of corresponding and alternate interior, students may use tracing paper and some of the strategies found earlier in the unit. Make sure to leave enough time for the next activity, “Alternate Interior Angles are Congruent.”Īs students work with their partners, they begin to fill in supplementary angles and vertical angles. The last two questions in this activity are optional, to be completed if time allows. They also consider whether the relationships they found hold true for any two lines cut by a transversal. ![]() Students investigate whether knowing the measure of one angle is sufficient to figure out all the angle measures in this situation. In this task, students explore the relationship between angles formed when two parallel lines are cut by a transversal line.
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