PTA (Parallel Lines, Transversals and Angles)

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Objective

SWBAT identify and apply relationships created by angles formed by parallel lines cut by a transversal.

Big Idea

Students will draw and measure to discover relationships of angles formed by parallel lines cut by a transversal.

Lesson Author

Stephanie Conklin

Saratoga Springs, NY

Grade Level

Tenth grade

Subjects

Math

Geometry

Standards

8.G.A.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

HSG-CO.C.9

Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

MP3

Construct viable arguments and critique the reasoning of others.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

Do Now

10 minutes

Students will review identifying angles like alternate interior, alternate exterior, corresponding, and consecutive interior angles. You should note that question #3 has none of these relationships.

Exploration #1 and #2

35 minutes

Flow of the Explorations

Reflection of Explorations 1 and 2_PTA Lesson.wmv

The video narrative explains the two explorations and how they exemplify math practice standards 3 (viable arguments and critiques) and 6 (attend to precison).

Practice with Angles

15 minutes

Teachers can lead students through these application with algebra questions for further practice of using angle relationships given 2 parallel lines cut by a transversal. Question #1 focuses on numerical application, while questions #2-4 focus on utilizing algebra skills. You should be wary of question #3 as most students will find x, and then stop. This is a great chance for you to warn students about this "trap" which is frequently on the SATs as well.

Activity/Homework

10 minutes

Students will work in small groups or independently to complete the activity if time remains. If time is limited in class this can become a homework assignment.