Page 147 - IM_FL_Geometry_Print Sample
P. 147
Student Response
• • • •
Student Lesson Summary
Our intuition leads us to believe that shortest path from a point to a line is along a perpendicular path. Can we be sure that our intuition is right in this case? Yes! The Pythagorean Theorem proves that this is the case.
We can call the length along the perpendicular , the length along a di erent path, , and the length between where those two paths meet the line, . It follows from the Pythagorean Theorem that
Because the two paths were di erent, we must have and therefore . It follows that . Since all lengths are positive . So any path that is not the perpendicular path is longer than the perpendicular path.
74
Teacher Guide
