Geometry 3-3 Complete Lesson: Proving Lines Parallel

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A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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Geometry 3-3 Complete Lesson: Proving Lines Parallel

Geometry 3-3 Complete Lesson: Proving Lines Parallel

Solve It! The maze has two intersecting sets of parallel paths. Follow the mouse's path through the maze. What is the measure of ∠1?Enter only a number.

Take Note: Summarize Theorem 3-4: The Converse of the Corresponding Angles Theorem. You may use the canvas to help illustrate your description.

Problem 1 Got It?

Take Note: Summarize Theorem 3-5: The Converse of the Alternate Interior Angles Theorem. You may use the canvas to help illustrate your description.

Take Note: Summarize Theorem 3-6: The Converse of the Same-Side Interior Angles Postulate. You may use the canvas to help illustrate your description.

Take Note: Describe flow proofs. How are they similar to two-column and paragraph proofs? How are they different?

Problem 2 Got It? Use the same diagram from Problem 2 to prove Theorem 3-6.Construct your flow proof using the tools on the canvas. You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 3 Got It? In Problem 3, what is another way to explain why r ∥s? Justify your answer.

Problem 4 Got It?

Theorems: Explain how you know when to use the Alternate Interior Angles Theorem and when to use the Converse of the Alternate Interior Angles Theorem.

Error Analysis: A classmate states that line AB is parallel to line DC based on the diagram here. Explain your classmate's error.

Review Lessons 1-6 and 3-1: Determine whether each statement is always, sometimes, or never true. Categorize them accordingly.

Review Lesson 3-2: Use the diagram below to find m\angle{1}. Enter only a number.

Review Lesson 3-2: Use the diagram below to find m\angle{2}. Enter only a number.

Vocabulary Review: Write the converse of the statement.If you are cold, then you wear a sweater.

Vocabulary Review: Write the inverse of the statement.If you are cold, then you wear a sweater.

Vocabulary Review: Write the contrapositive of the statement.If you are cold, then you wear a sweater.

Reflect: Math Success

Solve It! The maze has two intersecting sets of parallel paths. Follow the mouse's path through the maze. What is the measure of ∠1?Enter only a number.

What is the measure of ∠2?Enter only a number.

What is the measure of ∠3?Enter only a number.

What is the measure of ∠4?Enter only a number.

What is the measure of ∠5?Enter only a number.

Take Note: Summarize Theorem 3-4: The Converse of the Corresponding Angles Theorem. You may use the canvas to help illustrate your description.

Problem 1 Got It?

Take Note: Summarize Theorem 3-5: The Converse of the Alternate Interior Angles Theorem. You may use the canvas to help illustrate your description.

Take Note: Summarize Theorem 3-6: The Converse of the Same-Side Interior Angles Postulate. You may use the canvas to help illustrate your description.

Take Note: Summarize Theorem 3-7: The Converse of the Alternate Exterior Angles Theorem. You may use the canvas to help illustrate your description.

Take Note: Describe flow proofs. How are they similar to two-column and paragraph proofs? How are they different?

Problem 2 Got It? Use the same diagram from Problem 2 to prove Theorem 3-6.Construct your flow proof using the tools on the canvas. You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 3 Got It? In Problem 3, what is another way to explain why r ∥s? Justify your answer.

Problem 4 Got It?

Theorems: Explain how you know when to use the Alternate Interior Angles Theorem and when to use the Converse of the Alternate Interior Angles Theorem.

Error Analysis: A classmate states that line AB is parallel to line DC based on the diagram here. Explain your classmate's error.

Review Lessons 1-6 and 3-1: Determine whether each statement is always, sometimes, or never true. Categorize them accordingly.

Review Lesson 3-2: Use the diagram below to find m\angle{1}. Enter only a number.

Review Lesson 3-2: Use the diagram below to find m\angle{2}. Enter only a number.

Vocabulary Review: Write the converse of the statement.If you are cold, then you wear a sweater.

Vocabulary Review: Write the inverse of the statement.If you are cold, then you wear a sweater.

Vocabulary Review: Write the contrapositive of the statement.If you are cold, then you wear a sweater.

Reflect: Math Success

What is the measure of ∠2?Enter only a number.

What is the measure of ∠3?Enter only a number.

What is the measure of ∠4?Enter only a number.

What is the measure of ∠5?Enter only a number.

Take Note: Summarize Theorem 3-7: The Converse of the Alternate Exterior Angles Theorem. You may use the canvas to help illustrate your description.

Solve It! The maze has two intersecting sets of parallel paths. Follow the mouse's path through the maze. What is the measure of ∠1?
Enter only a number.

Problem 2 Got It? Use the same diagram from Problem 2 to prove Theorem 3-6.
Construct your flow proof using the tools on the canvas.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Vocabulary Review: Write the converse of the statement.
If you are cold, then you wear a sweater.

Vocabulary Review: Write the inverse of the statement.
If you are cold, then you wear a sweater.

Vocabulary Review: Write the contrapositive of the statement.
If you are cold, then you wear a sweater.

Solve It! The maze has two intersecting sets of parallel paths. Follow the mouse's path through the maze. What is the measure of ∠1?
Enter only a number.

What is the measure of ∠2?
Enter only a number.

What is the measure of ∠3?
Enter only a number.

What is the measure of ∠4?
Enter only a number.

What is the measure of ∠5?
Enter only a number.

Problem 2 Got It? Use the same diagram from Problem 2 to prove Theorem 3-6.
Construct your flow proof using the tools on the canvas.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Vocabulary Review: Write the converse of the statement.
If you are cold, then you wear a sweater.

Vocabulary Review: Write the inverse of the statement.
If you are cold, then you wear a sweater.

Vocabulary Review: Write the contrapositive of the statement.
If you are cold, then you wear a sweater.

What is the measure of ∠2?
Enter only a number.

What is the measure of ∠3?
Enter only a number.

What is the measure of ∠4?
Enter only a number.

What is the measure of ∠5?
Enter only a number.