Unit 1, Lesson 9
Transformations, Transversals, and Proof
Integrated Math 2
9.1
Warm-up
Lines and are parallel. Find the value of in each figure.
Figure A
Figure B
Figure C
Figure D
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Lines and are parallel. Find the value of in each figure.
Figure A
Figure B
Figure C
Figure D
Here are intersecting lines and :
Here are intersecting lines and :
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.