This preview shows page 1. Sign up to view the full content.
Unformatted text preview: AB (that is, CD forms a right angle with AB ), then this divides ABC into two smaller triangles CBD and ACD , which are both similar to ABC . A C B b a c D d c (a) ABC C D B d a (b) CBD A D C c d b (c) ACD Figure 1.1.5 Similar triangles ABC , CBD , ACD Recall that triangles are similar if their corresponding angles are equal, and that similarity implies that corresponding sides are proportional. Thus, since ABC is similar to CBD , by proportionality of corresponding sides we see that AB is to CB (hypotenuses) as BC is to BD (vertical legs) c a = a d cd = a 2 . Since ABC is similar to ACD , comparing horizontal legs and hypotenuses gives b c d = c b b 2 = c 2 cd = c 2 a 2 a 2 + b 2 = c 2 . QED Note: The symbols and denote perpendicularity and similarity, respectively. For example, in the above proof we had CD AB and ABC CBD ACD ....
View
Full
Document
This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Trigonometry

Click to edit the document details