Geometry: An Interactive Journey to Mastery



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H௘ͽ :KDWLVWKHPHDVXUHRIHDFKDQJOHLQDUHJXODUKHSWDJRQͼ௘VLGHG¿JXUH௘ͽ"
Solution
D௘ͽ ,IHDFKLQWHULRUDQJOHKDVPHDVXUHxWKHQxxx = 3x ƒIRUFLQJx ƒ
E௘ͽ $VTXDUHVXEGLYLGHVLQWRWZRWULDQJOHVDQGWKHUHIRUHKDVLQWHULRUDQJOHVVXPPLQJWRîƒ ƒ
,IHDFKLQWHULRUDQJOHRIWKHVTXDUHKDVPHDVXUHyWKHQy ƒJLYLQJy ƒ
F௘ͽ $SHQWDJRQVXEGLYLGHVLQWRWKUHHWULDQJOHVDQGWKHUHIRUHKDVLQWHULRUDQJOHVVXPPLQJWRîƒ 
ƒ,IHDFKLQWHULRUDQJOHRIDUHJXODUSHQWDJRQKDVPHDVXUHzWKHQz ƒJLYLQJz ƒ
G௘ͽ $KH[DJRQVXEGLYLGHVLQWRIRXUWULDQJOHVDQGWKHUHIRUHKDVLQWHULRUDQJOHVVXPPLQJWRîƒ ƒ
,IHDFKLQWHULRUDQJOHRIDUHJXODUKH[DJRQKDVPHDVXUHwWKHQw ƒJLYLQJw ƒ
H௘ͽ ,QWKHVDPHPDQQHUHDFKLQWHULRUDQJOHRIDUHJXODUKHSWDJRQKDVPHDVXUH ƒu 7 |ƒ
Study Tip
x 7KHUHLVYHU\OLWWOHQHHGWRPHPRUL]HIRUPXODV&OHDUXQGHUVWDQGLQJRILGHDVZLOODOORZ\RXWRTXLFNO\
UHFRQVWUXFWIRUPXODVLIWKH\DUHQHHGHG
Pitfall
x :KHQGLYLGLQJD¿JXUHLQWRWULDQJOHVLQRUGHUWRFRPSXWH
WKHVXPRILWVLQWHULRUDQJOHVEHVXUHWRDYRLGHUURQHRXV
LQWHULRUDQJOHVͼ௘6HHFigure 3.1௘ͽ

1. )LQGWKHPHDVXUHVRIDQJOHVx and y in Figure 3.2.


2. 2QHLQWHULRUDQJOHRIDWULDQJOHKDVPHDVXUHƒDQGDQRWKHUKDV
   PHDVXUHOHVVWKDQƒ:KDWFDQ\RXVD\DERXWWKHPHDVXUHRIWKH
   WKLUGLQWHULRUDQJOHRIWKHWULDQJOH"

40°

5 y

x y

x

Figure 3.

Figure 3.

180° 180°

180° 180° 180°

180°

180°

Problems