Geometry: An Interactive Journey to Mastery



Solution
'UDZDQ\OLQHWKURXJKWKHSRLQWLQWHUVHFWLQJWKHOLQHVHJPHQW
DQGPHDVXUHWKHDQJOHaͼ௘VKRZQLQFigure 7.5௘ͽLWKDSSHQVWRPDNH
:LWKDSURWUDFWRUGUDZDQRWKHUOLQHWKURXJKWKHSRLQW
PDNLQJWKHVDPHDQJOHaͼ௘6HHFigure 7.6௘ͽ
%HFDXVHZHKDYHFRQJUXHQWDOWHUQDWHLQWHULRUDQJOHV
ZHKDYHSDUDOOHOOLQHV
Study Tip
x ,WQHYHUKXUWVWRGUDZRYHUSDUWVRIFRPSOLFDWHG
GLDJUDPVZLWKFRORUHGSHQFLOV,I\RXKLJKOLJKWD
SDLURIOLQHVDQGDWUDQVYHUVDOIRUWKHPLWFDQEH
PXFKHDVLHUWRLGHQWLI\DOWHUQDWHLQWHULRUDQJOHV
DQGVDPHVLGHLQWHULRUDQJOHV
Pitfall
x 5HPHPEHUWKDWLQDSDLURIDOWHUQDWHLQWHULRU
DQJOHVHDFKDQJOH³WRXFKHV ́WKHVDPHWUDQVYHUVDO
EXWRQHDQJOHWRXFKHVRQHSDUDOOHOOLQHDQGWKHRWKHU
DQJOHWRXFKHVWKHRWKHUSDUDOOHOOLQH)RUH[DPSOH
LQWKHGLDJUDPLQFigure 7.7WKHDOWHUQDWHLQWHULRU
DQJOHWRd is xw.

1. $QJOHAIBKDVPHDVXUHƒ$QJOHDJKKDVPHDVXUHƒ
   )LQGWKHPHDVXUHVRIDQJOHVAIKGKFDQGGKI.

a

Figure 7.5

a

a

Figure 7.6

a

xw

bcd

Figure 7.7

Problems

A

B

C

D

E

G F

H

I

J

K

Figure 7.8