http://www.ck12.org Chapter 12. Rigid Transformations
The green triangle would be the final answer.
Investigation 12-2: Double Reflection over Intersecting Lines
Tools Needed: Example 7, protractor, ruler, pencil
- Take your answer from Example 7 and measure the angle of intersection for lineslandm. If you copied it
exactly from the text, it should be about 55◦. - Draw lines from two corresponding points on the blue triangle and the green triangle. These are the dotted
lines in the diagram below. - Measure this angle using your protractor. How does it related to 55◦?
Again, if you copied the image exactly from the text, the angle should be 110◦.
From this investigation, we see that the double reflection over two lines that intersect at a 55◦angle is the same as a
rotation of 110◦counterclockwise, where the point of intersection is the center of rotation. Notice that order would
matter in this composition. If we had reflected the blue triangle overmfollowed byl, then the green triangle would
be rotated 110◦clockwise.
Reflection over Intersecting Lines Theorem:If you compose two reflections over lines that intersect atx◦, then
the resulting image is a rotation of 2x◦, where the center of rotation is the point of intersection.
Notice that the Reflection over the Axes Theorem is a specific case of this one.
Example 8:Reflect the square overy=x, followed by a reflection over thex−axis.