A mathematics teacher likes to astound her students with tricks that can be explained through mathematics. Before the class studies similarity, the teacher brings a mirror to class and performs this trick: Note 3
The teacher puts the mirror on the floor facing up and asks a student to stand two feet from it. The teacher then positions herself so that she can just see the top of the student's head when she looks in the mirror. With a quick calculation, she reports the student's height. She's able to do the trick on every student in class.
Sketch the teacher, student, and mirror. Find a pair of similar triangles in your sketch, and explain how the teacher does her mirror trick. Note 4
It's important to know how mirrors work to understand this situation: The angle of incidence (the angle at which the light strikes the mirror) is equal to the angle of reflection (the angle at which the light leaves the mirror). Note 5Close Tip
Video Segment Similarity of triangles is frequently used in indirect measurement. In this segment, the participants watch a demonstration of the mirror trick and see how similarity of triangles can be used to estimate Brad's height. Watch this segment after you've completed Problem B1.
Think about why in this situation having the same angle measurement is enough to make two triangles similar.
If you are using a VCR, you can find this segment on the session video approximately 11 minutes and 27 seconds after the Annenberg Media logo.
To further explore similar triangles, go to Learning Math: Measurement, Session 5