Part 1: Exploring Parallel Lines Cut By A Transversal
Objective: I can use informal arguments to form conclusions about angle relationships created when parallel lines are cut by a transversal.
Figure 1
1) Here, we observe two parallel lines f and g cut by segment EF. Click on point E and move it to the left and to the right. Observe the measures of angles EGB and FHC. What do you observe?
3) What are some other angles with measures congruent to EGB and FHC. Select all that apply.
Figure 2
1) Here we again observe two parallel lines cut by a transversal. Click on Point E and move it to the left and to the right. What do you observe about the sum of the measures of angles EGA and FHC?
3) What are some other pairs of angles with the same relationship as angles EGA and FHC? Explain how you know.
4) When two parallel lines are cut by one transversal, how many total angle measures will there be in the entire figure, assuming no other lines or segments are present?
1) In this example, our two lines are not parallel. Drag Point E to the left and to the right as you have in the previous examples. What is different about this figure? How does it affect the observations you made in the previous examples?
Figure 3
2) Look at angles BGH and EGA. Why do these angles remain congruent even though the two lines are not parallel? Make a specific distinction between the relationships observed in the first two figures and this figure.