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Learning Math Home
Geometry Session 4, Part A: Introduction to Geometer's Sketchpad
 
Session 4 Part A Part B Part C Part D Homework
 
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Session 4 Materials:
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Session 4, Part B:
Parallel Lines (45 minutes)

In This Part: Properties of Angles | Reasoning About Properties of Angles

Parallel lines are two lines in the same plane that never intersect. Another way to think about parallel lines is that they are "everywhere equidistant." No matter where you measure, the perpendicular distance between two parallel lines is constant. With dynamic geometry software, you can draw two lines that look parallel, but you can't be sure that they are parallel unless you construct them to be parallel. Note 2

Problem B1

Solution  

Follow these steps to construct two parallel lines:

a. 

Using the Line Tool in Geometer's Sketchpad, draw a line.

b. 

Pull down the Construct menu in Sketchpad. You'll notice that the "Parallel Line" is gray -- therefore, not an option to you. This is Sketchpad's way of telling you that you don't have the correct objects selected or you don't have enough objects selected. What else do you need to construct a line parallel to your original line?

c. 

Continue your construction and record the steps you used to construct two parallel lines.


 

Problem B2

Solution  

Draw a transversal through your parallel lines. (A transversal is a line that passes through two parallel lines.)

transverse

a. 

Measure each of the angles formed.

b. 

Change the orientation of the transversal by dragging one of the defining points. Keep a record of what changes and what stays the same.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
To measure an angle, select three points in the order of the angle. You may need to construct additional points on your lines before you can measure the angles.   Close Tip

 
 

transverse

When a pair of parallel lines is cut by a transversal, several special pairs of angles are formed.

angleABD and angleEFB are corresponding angles.
angleABF and angleGFB are alternate interior angles.
angleABD and angleCBF are vertical angles.
angleABD and angleCBD form a linear pair.


 

Problem B3

Solution  

Name another pair of corresponding angles, another pair of alternate interior angles, another pair of vertical angles, and another linear pair.


 

Problem B4

Solution  

Using this new terminology, summarize the relationships you discovered in Problem B2.


Next > Part B (Continued): Reasoning About Properties of Angles

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