Lines and are parallel. Find the value of in each figure.
Figure A
Figure B
Figure C
Figure D
20.2
Activity
Make a Mark? Give a Reason
20.3
Activity
An Alternate Explanation
Student Lesson Summary
There are often several different ways to explain why statements are true. Comparing the different ways can lead to new insights or more flexible understanding. Consider the angles formed when 2 parallel lines and are cut by a transversal:
Suppose we want to explain why angle is congruent to angle . Label the midpoint of as . Rotating 180 degrees around takes angle to angle . Why? Well, and are equidistant from , so the rotation takes to . Also, it takes the transversal to itself, so it takes the ray to the ray . Finally, the rotation takes line onto line because 180-degree rotations take lines onto parallel lines, and is the only line parallel to that also goes through .
A different explanation can prove the same fact using a translation and the idea that vertical angles are congruent. Try thinking of that explanation yourself.
Glossary
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