Watford, M
Parallel Lines and Transversals Applet
Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
The slider controls the measure of Angle J. Drag the slider and explore what happens to the other angles as the measure of J is modified. Answer the questions below. |
Explore the following theorems:
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- Given that the two horizontal lines are parallel, show that the Alternate Interior Angles theorem is true Use previous theorems learned concerning angles to prove the theorem.
- Make J be a right angle. What happens to the other angles? What theorems can describe what happens in this case?
- Drag the slider to explore angle measures. What do you notice about the sums of angles that lie along a common line?
- Explain why the sum of those angles is consistent
- Using your previous observances, prove the Alternate Exterior Angles theorem.
- Which sets of four angles are always congruent by our theorems?
- Given that the measure of J is 60°, what are the measures of angles, P, K and M? Justify your answer using the theorems discussed. Validate that your answers are correct using the above tool.
- Choose another angle measure and find measures of angles O, P, and Q. Justify your answers using the same process as above.