Chapter 2
Angles and Parallel Lines
Two straight paths on a map may seem to run alongside each other, but the drawing cannot show where they would go forever. Could the angles where a third path crosses both help you decide whether the paths are parallel? You may already know how to calculate missing angles. Now the question is why an angle relationship must hold, and whether reversing a claim gives a reliable test. Angles and parallel lines offer a new setting for deciding what the information in a diagram can justify.
What You'll Explore
5 lessons.
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When two lines cross, how much can one angle tell you about the others? Investigate which angle pairs can be linked by their positions or measures, and what makes a relationship hold for every such crossing.
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A line crossing two parallel lines creates angles at different places. Which of them are connected, and what changes if the lines stop being parallel? Explore how the given line relationships support conclusions about angles, even when the drawing is tilted.
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Can angle information establish that two lines are parallel or perpendicular? Examine which conditions settle the question, which leave it open, and how a parallel through a point outside a given line could be drawn.
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Try sketching triangles that look as different as possible. Can their angles vary freely, or are there restrictions that every triangle must obey? Investigate what the angles can tell you about the kind of triangle you have.
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What can you learn by continuing one side of a triangle past a corner? Explore connections between the new angle and the triangle's other corners, then consider the turns made around its boundary.