Geometry 3-4 Parallel and Perpendicular Lines

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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 3-4 Parallel and Perpendicular Lines

Geometry 3-4 Parallel and Perpendicular Lines

Solve It! Jude and Jasmine leave school together to walk home. Then Jasmine cuts down a path from Schoolhouse Road to get to Oak Street and Jude cuts down another path to get to Court Road. What conjecture can you make about Oak Street and Court Road?

Explain. You may use the canvas to help illustrate your explanation.

Take Note: Summarize Theorem 3-8. You may use the canvas to help illustrate your description.

Take Note: Summarize Theorem 3-9. You may use the canvas to help illustrate your description.

Problem 1 Got It? Can you assemble the pieces to form a picture frame with opposite sides parallel? Justify your reasoning on the canvas using text and/or illustrations.

Take Note: Summarize Theorem 3-10. You may use the canvas to help illustrate your description.

Problem 2 Got It? In Problem 2, could you also conclude a ∥b? Explain your reasoning on the canvas using text and/or illustrations.

Design: Draw a diagram to model the situation.◆ Main street intersects Avenue A and Avenue B. ◆ Avenue A is parallel to Avenue B. ◆ Avenue A is also perpendicular to Main Street.Be sure to include relevant details.

Consider the situation from the previous item.◆ Main street intersects Avenue A and Avenue B.◆ Avenue A is parallel to Avenue B.◆ Avenue A is also perpendicular to Main Street.How are Avenue B and Main Street related?

In the diagram, lines a, b, and c are coplanar. What conclusion can you make about lines a and b? Explain.You may use the canvas to help illustrate your explanation.

Vocabulary: Explain why the phrase in a plane is not necessary in Theorem 3-8.

Error Analysis: Sally sketched coplanar lines m, n, and r on her homework paper. She claims that it shows that lines m and n are parallel. What other information do you need about line r in order for Sally's claim to be true? Explain.

Review Lesson 3-3: Determine the value of x for which a∥b.

Review Lesson 3-3: Determine the value of x for which a∥b. Enter only a number.

Review Lesson 1-4.

Additional Vocabulary Support: Parallel and Perpendicular Lines.Categorize the figures described in each scenario. Each category should contain only one item.

Vocabulary Review: Complete each statement on the right with always, sometimes, or never from the left.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.If a < b and b < c, then __?__.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.If Joe is younger than Ann and Ann is younger than Sam, then __?__.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.If you travel from Station 2 to Station 3 and you travel from __?__, then you travel from Station 2 to Station 4.

Reflection: Math Success

Solve It! Jude and Jasmine leave school together to walk home. Then Jasmine cuts down a path from Schoolhouse Road to get to Oak Street and Jude cuts down another path to get to Court Road. What conjecture can you make about Oak Street and Court Road?

Explain. You may use the canvas to help illustrate your explanation.

Take Note: Summarize Theorem 3-8. You may use the canvas to help illustrate your description.

Take Note: Summarize Theorem 3-9. You may use the canvas to help illustrate your description.

Problem 1 Got It? Can you assemble the pieces to form a picture frame with opposite sides parallel? Justify your reasoning on the canvas using text and/or illustrations.

Take Note: Summarize Theorem 3-10. You may use the canvas to help illustrate your description.

Problem 2 Got It? In Problem 2, could you also conclude a ∥b? Explain your reasoning on the canvas using text and/or illustrations.

Design: Draw a diagram to model the situation.◆ Main street intersects Avenue A and Avenue B. ◆ Avenue A is parallel to Avenue B. ◆ Avenue A is also perpendicular to Main Street.Be sure to include relevant details.

Consider the situation from the previous item.◆ Main street intersects Avenue A and Avenue B.◆ Avenue A is parallel to Avenue B.◆ Avenue A is also perpendicular to Main Street.How are Avenue B and Main Street related?

In the diagram, lines a, b, and c are coplanar. What conclusion can you make about lines a and b? Explain.You may use the canvas to help illustrate your explanation.

Vocabulary: Explain why the phrase in a plane is not necessary in Theorem 3-8.

Error Analysis: Sally sketched coplanar lines m, n, and r on her homework paper. She claims that it shows that lines m and n are parallel. What other information do you need about line r in order for Sally's claim to be true? Explain.

Review Lesson 3-3: Determine the value of x for which a∥b.

Review Lesson 3-3: Determine the value of x for which a∥b. Enter only a number.

Review Lesson 1-4.

Review Lesson 1-4.

Additional Vocabulary Support: Parallel and Perpendicular Lines.Categorize the figures described in each scenario. Each category should contain only one item.

Vocabulary Review: Complete each statement on the right with always, sometimes, or never from the left.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.If a < b and b < c, then __?__.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.If Joe is younger than Ann and Ann is younger than Sam, then __?__.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.If you travel from Station 2 to Station 3 and you travel from __?__, then you travel from Station 2 to Station 4.

Reflection: Math Success

Review Lesson 1-4.

Problem 1 Got It? Can you assemble the pieces to form a picture frame with opposite sides parallel?
Justify your reasoning on the canvas using text and/or illustrations.

Problem 2 Got It? In Problem 2, could you also conclude a ∥b?
Explain your reasoning on the canvas using text and/or illustrations.

Design: Draw a diagram to model the situation.
◆ Main street intersects Avenue A and Avenue B.
◆ Avenue A is parallel to Avenue B.
◆ Avenue A is also perpendicular to Main Street.
Be sure to include relevant details.

Consider the situation from the previous item.
◆ Main street intersects Avenue A and Avenue B.
◆ Avenue A is parallel to Avenue B.
◆ Avenue A is also perpendicular to Main Street.
How are Avenue B and Main Street related?

In the diagram, lines a, b, and c are coplanar.
What conclusion can you make about lines a and b? Explain.
You may use the canvas to help illustrate your explanation.

Additional Vocabulary Support: Parallel and Perpendicular Lines.
Categorize the figures described in each scenario. Each category should contain only one item.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.
If a < b and b < c, then ?.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.
If Joe is younger than Ann and Ann is younger than Sam, then ?.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.
If you travel from Station 2 to Station 3 and you travel from ?, then you travel from Station 2 to Station 4.

Problem 1 Got It? Can you assemble the pieces to form a picture frame with opposite sides parallel?
Justify your reasoning on the canvas using text and/or illustrations.

Problem 2 Got It? In Problem 2, could you also conclude a ∥b?
Explain your reasoning on the canvas using text and/or illustrations.

Design: Draw a diagram to model the situation.
◆ Main street intersects Avenue A and Avenue B.
◆ Avenue A is parallel to Avenue B.
◆ Avenue A is also perpendicular to Main Street.
Be sure to include relevant details.

Consider the situation from the previous item.
◆ Main street intersects Avenue A and Avenue B.
◆ Avenue A is parallel to Avenue B.
◆ Avenue A is also perpendicular to Main Street.
How are Avenue B and Main Street related?

In the diagram, lines a, b, and c are coplanar.
What conclusion can you make about lines a and b? Explain.
You may use the canvas to help illustrate your explanation.

Additional Vocabulary Support: Parallel and Perpendicular Lines.
Categorize the figures described in each scenario. Each category should contain only one item.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.
If a < b and b < c, then ?.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.
If Joe is younger than Ann and Ann is younger than Sam, then ?.

Use Your Vocabulary: Complete the statement so that it is an example of the Transitive Property.
If you travel from Station 2 to Station 3 and you travel from ?, then you travel from Station 2 to Station 4.