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Parallel Lines and Transversals
Pacing:This lesson should take one class period
Goal:The textbook further extends the notion of transversals and parallel lines to illustrate the corresponding angles
postulate and the alternate interior angles postulate. Additional theorems and postulates are proven in this lesson.
Use the in-class activity from the previous lesson as a refresher and guide to the lesson opener. This lesson
provides several key theorems: corresponding angles postulate and alternate interior angles postulate. Students
have experienced the definitions of these angles in previously lessons and have also been given brief introductory
proofs. The goal of this lesson is to use these notions to prove alternate exterior angles are congruent and consecutive
interior angles of parallel lines are supplementary.
In-Class Activity!Divide your class into six sections of pairs. Provide enough copies of the Corresponding Angles
Postulate, its converse, the Alternate Interior Angles Postulate, its converse, and the Alternate Exterior Angles
Postulate and its converse. Instruct each pair to prove their theorem, and then group homogenous sections in order
to discuss the results. Taking a pair of each theorem and its respective converse to form a team of four, have the
students discuss the proofs. As an assignment, have the groups create a visual poster of the proof of the theorem, the
converse and its respective proof.
In-Class Activity! Demonstrate to students that these theorems do not apply to non-parallel lines. Each student
should create two non-parallel lines and a transversal. Label the 8 angles formed, having students measure all
angles. Students will see the alternate interior angles, corresponding angles, and vertical angles are not congruent,
nor are the consecutive interior angles supplementary.
Proving Lines Parallel
Pacing:This lesson should take one class period
Goal: The converse of the previous lesson’s theorems and postulates are provided in this lesson. Students are
encouraged to read through this lesson and follow along with the proofs.
Vocabulary!The Parallel Lines Property can be stated, “If linelis parallel to linem, and linemis parallel to linen,
then lineslandnare also parallel.” Ask students to write the converse of this property and determine if it is true. If
students determine the converse false, have them provide a counterexample.
Chapter 1. Geometry TE - Teaching Tips