Developing Transversal Intuition

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SWBAT connect the concepts of vertical and supplementary angles to interpret the relationships between angles formed by a transversal.

Big Idea

Students get a change to make informal arguments about angles and explain why and when angles will be equal when they are cut by a transversal.

Lesson Beginning

15 minutes

Today I want to keep it simple. I present a simple diagram of a transversal:


I ask students to measure all of the angles in the diagram. When I feel the class is ready, I ask them “how did I (or a student) solve this by only measuring one angle.”  I use this as a launching point to discuss many different features of angles and transversals.

Many students are able to reason with the help of the transitive property, vertical angles and supplementary angles that alternate interior and exterior angles must be equal. Although you will certainly spend some time defining math vocabulary, don’t force the conversation around these angles being equal. If students aren’t able to articulate why alternate interior and exterior angles are equal, you can get back to in later in the lesson.

Lesson Middle

30 minutes

Next, I ask my students to practice mild, medium and spicy problems from the Transversal Spice Rack. As they work I circulate with a purpose. I want to gather information for a summary discussions.  I am on the lookout for particularly interesting examples of student work.  

Extensions and Scaffolds:  If necessary, I make the discussion at the end of this section more accessible to my students by providing handout with diagrams of transversals that accompany my introductory presentation.  I do not want students spending a tremendous amount of time setting up and labeling the points and angles of a diagram. Check the video, Teach_Students_to_Decompose_a_Transversal, for some helpful themes around this lesson.


Lesson End

20 minutes

To end the lesson, I have students present their solutions to the problems they solved. As they do, we discuss ideas around angles and transversal lines. I pay attention to whether students use vocabulary appropriately and make valid inferences (MP2, MP6). I am on the lookout for students who are using the idea that the corresponding angles will also be equal.  In order to ground the discussion, I may return to the question of when and why angles cut by a transversal are equal or not equal.