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Angles and Parallel Lines
Stepbystep directions for constructing
and investigating angles in relation to parallel lines
using Geometer's Sketchpad.

Investigating angles with parallel and nonparallel lines. 


1. Set Preferences: Under
Edit, choose "Preferences", the "Units" Tab (indicate cm
and hundredths), "Text" Tab (if necessary,
turn off the automatic labeling = uncheck box under "Show Label
Automatically" in front of "for all new points") and "Color" Tab (pick any color
choices).
5. Points of intersection: Establish the two points of intersection where the transversal crosses the first two lines. Choose the Select Tool, , click to highlight line AB and line EF, choose Construct menu, option Intersection. Label the point. Repeat for CD and EF. (You can also establish the intersection point by using the point tool.) 6. Measure angles: Choose the Select Tool, click to highlight the three points of any angle whose vertex is one of the two points of intersection with the transversal. From the Measure menu, choose Angle. Repeat for all eight angles. Arrange the angle measures appropriately on the screen. At this point you should see a diagram similar to:
7. Stop and Observe: The lines in this drawing are not parallel. What observations can be made regarding the alternate interior angles, the corresponding angles, the interior angles on the same side of the transversal, the alternate exterior angles, the vertical angles, and the angles forming linear pairs? 8. Draw Parallel Lines: Choose the Select tool, highlight line CD. Under Edit, choose Cut. Highlight the intersection point E and line AB. Choose the Construct menu, Parallel Line. 9. Measure Angles: Measure the eight angles again. 10. Stop and Observe: The lines in this drawing are parallel. What observations can be made regarding the alternate interior angles, the corresponding angles, the interior angles on the same side of the transversal, the alternate exterior angles, the vertical angles, and the angles forming linear pairs? 11. Complete the observation sheet. Please check out Terms of Use.

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