Geometry: An Interactive Journey to Mastery

Solutions

2. 'UDZDGLDJRQDODQGODEHOWKHVLGHVb 1 DQGb 2 DVVKRZQ
   LQFigure S.14.2
   L 7KHDQJOHVPDUNHGZLWKDGRWDUHFRQJUXHQWEHFDXVH
   WKH\DUHDOWHUQDWHLQWHULRUDQJOHVIRUSDUDOOHOOLQHV
   LL 7KHWZRWULDQJOHVZHVHHDUHVLPLODUE\6$6ͼ௘WKHVLGH
   ODEHOHGaWKHDQJOHODEHOHGZLWKDGRWDQGWKHVKDUHGGLDJRQDO௘ͽ
   LLL 7KHWULDQJOHVDUHFRQJUXHQWEHFDXVHWKHVFDOHIDFWRULVFOHDUO\
   LY 7KXVb 1  b 2 EHFDXVHWKH\DUHPDWFKLQJVLGHVLQFRQJUXHQWWULDQJOHV
   Y 7KH¿JXUHLVDSDUDOOHORJUDPEHFDXVHRIWKHSUHYLRXVSUREOHPͼ௘:HMXVWVKRZHGWKDWERWKSDLUVRI
   RSSRVLWHVLGHVDUHFRQJUXHQW௘ͽ


3. L EB DF& EHFDXVHRSSRVLWHHGJHVRIDSDUDOOHORJUDP
   DUHSDUDOOHO
   LL AB CDEHFDXVHRSSRVLWHHGJHVRIDSDUDOOHORJUDP
   DUHFRQJUXHQW
   LLLEBABDFDC 2211 DQG EHFDXVHEDQGF
   DUHPLGSRLQWV
   LY EB DFEHFDXVHRIVWHSVDQG
   Y EBFDLVDSDUDOOHORJUDPEHFDXVHLWKDVRQHSDLURIRSSRVLWHHGJHVWKDWDUHERWKFRQJUXHQWDQGSDUDOOHO


4. D௘ͽ 7KHIDFWWKDWVDPHVLGHLQWHULRUDQJOHVPXVWDGGWRƒLQWKHSUHVHQFHRISDUDOOHOOLQHVIRUFHV
   WZRPRUHLQWHULRUDQJOHVWREHULJKWDQJOHV7KHIDFWWKDWDOODQJOHVLQDTXDGULODWHUDOVXPWRƒ
   IRUFHVWKHIRXUWKDQJOHWREHULJKWDVZHOO:HWKXVKDYHD¿JXUHZLWKIRXUULJKWDQJOHV,WLVDUHFWDQJOH
   E௘ͽ 2SSRVLWHVLGHVLQDSDUDOOHORJUDPDUHFRQJUXHQW7KLVIRUFHVDOOIRXUVLGHVWREHFRQJUXHQW:HKDYH
   DUKRPEXV

a

a

b 1 b 2

Figure S.14.2

AB

DFC

E

Figure S.14.3