Geometry 3-3 Complete Lesson: Proving Lines Parallel
By Matt Richardson
Last updated about 2 years ago
27 Questions
Note from the author:
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.
2
1.
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.
2
2.
What is the measure of ∠2?
Enter only a number.
2
3.
What is the measure of ∠3?
Enter only a number.
2
4.
What is the measure of ∠4?
Enter only a number.
2
5.
What is the measure of ∠5?
Enter only a number.
10
6.
Take Note: Summarize Theorem 3-4: The Converse of the Corresponding Angles Theorem. You may use the canvas to help illustrate your description.
10
7.
Problem 1 Got It?
G.CO.9
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8.
Take Note: Summarize Theorem 3-5: The Converse of the Alternate Interior Angles Theorem. You may use the canvas to help illustrate your description.
10
9.
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.
10
10.
Take Note: Summarize Theorem 3-7: The Converse of the Alternate Exterior Angles Theorem. You may use the canvas to help illustrate your description.
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11.
Take Note: Describe flow proofs. How are they similar to two-column and paragraph proofs? How are they different?
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12.
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.
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13.
Problem 3 Got It? In Problem 3, what is another way to explain why r ∥s? Justify your answer.
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14.
Problem 4 Got It?
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15.
G.CO.9
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16.
G.CO.9
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17.
10
18.
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.
G.CO.9
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19.
Error Analysis: A classmate states that line AB is parallel to line DC based on the diagram here. Explain your classmate's error.
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20.
Review Lessons 1-6 and 3-1: Determine whether each statement is always, sometimes, or never true. Categorize them accordingly.
- Two lines in intersecting planes are perpendicular.
- Perpendicular lines meet at right angles.
- Two lines in parallel planes are perpendicular.
- Two lines in the same plane are parallel.
- Always
- Sometimes
- Never
10
21.
Review Lesson 3-2: Use the diagram below to find m\angle{1}. Enter only a number.
10
22.
Review Lesson 3-2: Use the diagram below to find m\angle{2}. Enter only a number.
5
23.
Vocabulary Review: Write the converse of the statement.
If you are cold, then you wear a sweater.
5
24.
Vocabulary Review: Write the inverse of the statement.
If you are cold, then you wear a sweater.
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25.
Vocabulary Review: Write the contrapositive of the statement.
If you are cold, then you wear a sweater.
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26.
Use Your Vocabulary: Complete each sentence on the right with interior or exterior from the left.
Refer to the diagram for some items.
You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.
- exterior
- interior
- In the diagram, angles 1 and 7 are alternate __?__ angles.
- In the diagram, angles 4 and 5 are same-side __?__ angles.
- To paint the outside of your house, buy __?__ paint.
- The protective cover prevents the __?__ of the book from being damaged.
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27.
Reflect: Math Success