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Student Exploration: Parallel, Intersecting, and Skew Lines Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: intersecting lines, line, parallel lines, plane, point, skew lines Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. A point is a specific location in space. A line is a straight path that extends forever in both directions. Line AB ( AB ) shown to the right contains points A and B. How many other points do you think AB contains? Why? 2. A plane is a flat surface that extends forever in all directions. How many lines do you think a plane contains? Why? Gizmo Warm-up In the Parallel, Intersecting, and Skew Lines Gizmo, you will explore relationships between lines in the same plane and between lines in different planes. With One line selected from the dropdown menu, click on the plane to stop its rotation. 1. Click New line several times. How many different lines can be generated that all lie in this plane? 2. Click New plane a few times. How many different planes can be generated that contain this line? 3. A plane is "defined" if only one plane can be generated. Does one line define a plane? Why?Activity: Relationships between two lines get the Qizmg ready: 0 Select Intersecting lines. 1. Click on New lines several times. Drag the plane around as needed to view the lines. A. The lines _. How many points do the lines have in common? _ B. Click New plane a few times. Does the plane change? _ C. In your own words, describe intersecting lines. 2. Click New example several times. For each new example, click New plane. A. Is it possible for more than one plane to contain a pair of intersecting lines? |:| B. Does a pair of intersecting lines dene a plane? U Explain. 3. Select Parallel lines. Drag the plane until it appears to be nearly at. Then click New lines several times, dragging the plane each time. A. The lines are -. How many points do parallel lines have in common? B. Click New plane a few times. Does the plane change? C. In your own words, describe parallel lines. 4. Click New example several times. For each new example, click New plane. U A. Is it possible for more than one plane to contain a pair of parallel lines? Explain. B. Does a pair of parallel lines dene a plane? U Explain. 5. Select Skew lines. Drag the plane around to see different views. Then click New line several times, dragging the plane each time. A. The two lines shown each time are -. Do skew lines ever intersect? B. Click New plane a few times. How many of the lines lie in the new plane? _ U] C. In your own words. describe skew lines. 6. Click New example several times. For each new example, click New plane. A. Are skew lines ever in the same plane? B. Does a pair of skew lines dene a plane? _ U] Explain. 7. Neither parallel lines nor skew lines ever intersect. What are the differences between parallel lines and skew lines? 8. Can two lines that lie in the same plane be anything but intersecting or parallel? Explain. H 9. The gure below contains several different pairs of intersecting, parallel, and skew lines. A. Name three different pairs of intersecting lines. Egg B. Name three different pairs of parallel lines. :_E E 0. Name three different pairs of skew lines. SE
