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# Applying Postulates and Theorems Involving Parallel Lines Cut by a Transversal

Lesson 6 of 9

## Objective: SWBAT solve problems involving parallel lines cut by a transversal providing justification for their solution processes.

#### Activating Prior Knowledge

*15 min*

**Where We've Been:** We've just finished proving theorems about angles created when parallel lines are cut by a transversal.

**Where We're Going:** These theorems will be used in several contexts later in the course. In the near future, we'll use the alternate interior angles theorem to help us prove that the interior angle measures of a triangle sum to 180 degrees.

For this section, students get to work on the Activating Prior Knowledge:PLCT resource. When students are finished (5-10 minutes), I go over the correct answers on the document camera.

#### Resources

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#### Modeling

*20 min*

For this section, I model the first problem from the PLCT_Problem Solving with Justification[Model] resource. I model the correct solution process, but more importantly, how to show and explain the solution.

Once I've modeled that problem, we're ready to move on to the next section.

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#### Independent Practice

*40 min*

In this section, students try their hand at solving some problems involving parallel lines cut by a transversal. For this section, I use the PLCT_Problem Solving with Justification[Student] resource. There are four problems in total on the handout. I make double-sided copies but do not staple them. I like to hand out only problems 1 and 2 to the whole class at first. For many students, in my experience, doing a quality job on those two problems will require all of the allotted time.

A good number of students who say that they are finished end up needing some feedback and refinement before they produce a finished product.

For those students who are more advanced and achieve a finished product on problems 1 and 2, I keep problems 3 and 4 ready. These problems involve quadratic equations and systems of linear equations. This provides a good challenge and makes for a teachable moment in which I get to hone some important algebra skills.

Problems 2 through 4 from the PLCT_Problem Solving with Justification[Model] resource are also available for students who finish the entire handout.

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- UNIT 1: Community Building, Norms, and Expectations
- UNIT 2: Geometry Foundations
- UNIT 3: Developing Logic and Proof
- UNIT 4: Defining Transformations
- UNIT 5: Quadrilaterals
- UNIT 6: Similarity
- UNIT 7: Right Triangles and Trigonometry
- UNIT 8: Circles
- UNIT 9: Analytic Geometry
- UNIT 10: Areas of Plane Figures
- UNIT 11: Measurement and Dimension
- UNIT 12: Unit Circle Trigonmetry
- UNIT 13: Extras

- LESSON 1: Vertical Angles and Linear Pairs
- LESSON 2: Conjecture is Not Enough: The need for proof
- LESSON 3: Deductive Reasoning and Proof
- LESSON 4: Developing Two-Column Proof Skills
- LESSON 5: Exploring Parallel Lines Cut By a Transversal
- LESSON 6: Applying Postulates and Theorems Involving Parallel Lines Cut by a Transversal
- LESSON 7: Proving Theorems involving Parallel Lines Cut by a Transversal
- LESSON 8: Making Conjectures about the Midsegments of a Triangle
- LESSON 9: Proving Theorems About Triangles