Geometry 3-6 Complete Lesson: Constructing Parallel and Perpendicular Lines

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Solve It!

1. Draw a line m on a sheet of paper.
2. Fold your paper so that line m falls on itself.
3. Label the fold line n.
4. Fold your paper again so that n falls on itself.
5. Label your new fold line p.
6. Take a picture of your paper and upload it to the canvas.

How are m and p related? How do you know?

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Take Note: Summarize the process of constructing a line parallel to a given line. You may use the canvas to help illustrate your description.

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Problem 1 Got It?

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Problem 2 Got It?
1. Complete the construction below on the embedded GeoGebra utility (or at geogebra.org/geometry)
a. Draw a segment.
b. Label its length m.
c. Construct a quadrilateral ABCD with \overleftrightarrow{AB}||\overleftrightarrow{CD}, so that AB=m and CD=2m.

2. Screenshot your final product.
3. Upload your screenshot to the canvas.
4. Ensure that your screenshot fills the canvas.

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Take Note: Summarize the process of constructing a perpendiculr at a point to a line. You may use the canvas to help illustrate your description.

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Problem 3 Got It?

1. On paper, use a straightedge to draw line EF. (Take a clear picture to document your work)
2. Construct line FG so that line FG is perpendicular to line EF at point F.
Be sure to leave marks as evidence of your construction techniques.
(Take a clear picture to document your work)
3. Upload your images to the appropriate locations on the canvas.

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Take Note: Summarize The Perpendicular Postulate. You may use the canvas to help illustrate your description.

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Take Note: Summarize the process of constructing a perpendicular from a point to a line. You may use the canvas to help illustrate your description.

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Problem 4 Got It?

1. On paper, use a straightedge to draw line CX and a point Z not on line CX.
(Take a picture to document your work)
2. Construct line ZB so that line ZB is perpendicular to line CX.
Be sure to leave marks as evidence of your construction techniques.
(Take a picture to document your work)
3. Upload your images to the appropriate locations on the canvas.

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1. Use GeoGebra or paper with a traditional compass and straightedge to complete the construction below.
2. Take screenshots or pictures to document your process.
3. Add the images to the canvas below in chronological order.

Construction: Draw a line l and a point P not on the line. Construct the line through P parallel to line l.

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1. Use GeoGebra or paper with a traditional compass and straightedge to complete the construction below.
2. Take screenshots or pictures to document your process.
3. Add the images to the canvas below in chronological order.

Construction: Draw line QR and a point S on the line. Construct the line perpendicular to line QR at point S.

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1. Use GeoGebra or paper with a traditional compass and straightedge to complete the construction below.
2. Take screenshots or pictures to document your process.
3. Add the images to the canvas below in chronological order.

Construction: Draw line w and a point X not on the line. Construct the line perpendicular to line w at point X.

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In problem 3, is segment AC congruent to segment BC? Explain.

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Compare and Contrast: How are the constructions in Problems 3 and 4 similar? How are they different? You may use the canvas to help illustrate your explanations.

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Review Lesson 3-5. Find the value of x. Enter only a number.

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Review Lesson 3-5. Find the value of y. Enter only a number.

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Review Arithmetic: Simplify the ratio.

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Review Arithmetic: Simplify the ratio.
Enter only a number.

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Review Arithmetic: Simplify the ratio.
Enter only a number.

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Vocabulary Review: True or False: A rectangle has two pairs of parallel segments.

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Vocabulary Review: True or False: A rectangle has two pairs of perpendicular segments.

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Vocabulary Review: Consider the diagrams below and categorize each pair of angles.

∠3 and ∠4
∠1 and ∠2
∠5 and ∠6

Alternate exterior
Alternate interior
Corresponding

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Use Your Vocabulary: Match each statement on the right with the correct form of the word construction.

Draggable item		Corresponding Item
construct (VERB)		You __?__ sand castles at the beach.
construction (NOUN)		The __?__ on the highway caused quite a traffic jam.
constructive (ADJECTIVE)		The time you spent working on your homework was __?__.

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Reflect: Math Success

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Geometry 3-6 Complete Lesson: Constructing Parallel and Perpendicular Lines

Take Note: Summarize the process of constructing a line parallel to a given line. You may use the canvas to help illustrate your description.

Problem 1 Got It?

Take Note: Summarize the process of constructing a perpendiculr at a point to a line. You may use the canvas to help illustrate your description.

Take Note: Summarize The Perpendicular Postulate. You may use the canvas to help illustrate your description.

Take Note: Summarize the process of constructing a perpendicular from a point to a line. You may use the canvas to help illustrate your description.

In problem 3, is segment AC congruent to segment BC? Explain.

Compare and Contrast: How are the constructions in Problems 3 and 4 similar? How are they different? You may use the canvas to help illustrate your explanations.

Review Lesson 3-5. Find the value of x. Enter only a number.

Review Lesson 3-5. Find the value of y. Enter only a number.

Review Arithmetic: Simplify the ratio.

Review Arithmetic: Simplify the ratio.Enter only a number.

Review Arithmetic: Simplify the ratio.Enter only a number.

Vocabulary Review: True or False: A rectangle has two pairs of parallel segments.

Vocabulary Review: True or False: A rectangle has two pairs of perpendicular segments.

Vocabulary Review: Consider the diagrams below and categorize each pair of angles.

Use Your Vocabulary: Match each statement on the right with the correct form of the word construction.

Reflect: Math Success

Take Note: Summarize the process of constructing a line parallel to a given line. You may use the canvas to help illustrate your description.

Problem 1 Got It?

Take Note: Summarize the process of constructing a perpendiculr at a point to a line. You may use the canvas to help illustrate your description.

Take Note: Summarize The Perpendicular Postulate. You may use the canvas to help illustrate your description.

Take Note: Summarize the process of constructing a perpendicular from a point to a line. You may use the canvas to help illustrate your description.

In problem 3, is segment AC congruent to segment BC? Explain.

Compare and Contrast: How are the constructions in Problems 3 and 4 similar? How are they different? You may use the canvas to help illustrate your explanations.

Review Lesson 3-5. Find the value of x. Enter only a number.

Review Lesson 3-5. Find the value of y. Enter only a number.

Review Arithmetic: Simplify the ratio.

Review Arithmetic: Simplify the ratio.Enter only a number.

Review Arithmetic: Simplify the ratio.Enter only a number.

Vocabulary Review: True or False: A rectangle has two pairs of parallel segments.

Vocabulary Review: True or False: A rectangle has two pairs of perpendicular segments.

Vocabulary Review: Consider the diagrams below and categorize each pair of angles.

Use Your Vocabulary: Match each statement on the right with the correct form of the word construction.

Reflect: Math Success

Review Arithmetic: Simplify the ratio.
Enter only a number.

Review Arithmetic: Simplify the ratio.
Enter only a number.

Review Arithmetic: Simplify the ratio.
Enter only a number.

Review Arithmetic: Simplify the ratio.
Enter only a number.