Geometry: An Interactive Journey to Mastery

Solutions

Lesson 10

1. D௘ͽ 7KHUHLVQRUHDVRQWREHOLHYHWKDWWKHVHWULDQJOHVDUHVLPLODU
   E௘ͽ 0DUNFRQJUXHQWDOWHUQDWHLQWHULRUDQJOHVIRUSDUDOOHOOLQHV
   DVVKRZQLQFigure S.10.1
    7KHWZRWULDQJOHVDUHVLPLODUE\$$%HFDXVHWKH\VKDUH
   WKHGLDJRQDOͼ௘ZKLFKGRHVFRUUHVSRQGWRPDWFKLQJVLGHV
   LQWKHWZRWULDQJOHV௘ͽWKHVFDOHIDFWRULV7KHWULDQJOHVDUH
   LQIDFWFRQJUXHQW
   F௘ͽ /DEHOWKHVLGHVa 1 DQGa 2 DVVKRZQLQFigure S.10.2
    %\WKH3\WKDJRUHDQWKHRUHPaxh 1 ^22 DQGaxh 2 ^22 ;
   WKXVa 1  a 2 7KHWZRWULDQJOHVDUHVLPLODUE\666ZLWKVFDOHIDFWRU
   7KH\DUHLQIDFWFRQJUXHQW
   G௘ͽ 6HHFigure S.10.3$QJOHVODEHOHGxDUHFRQJUXHQWEHFDXVHWKH\DUH
   YHUWLFDODQJOHV
    $QJOHVODEHOHGyDUHFRQJUXHQWEHFDXVHWKH\DUHDOWHUQDWHLQWHULRU
   DQJOHVIRUSDUDOOHOOLQHV
    7KHWZRWULDQJOHVDUHVLPLODUE\$$


2. /RRNDWWKHUDWLRRIWKHORQJHVWVLGHVk  

/RRNDWWKHUDWLRRIWKHVKRUWHVWVLGHVk (^)  7KHUHLVQRFRQVLVWHQWVFDOHIDFWRUIRUWKHVLGHV
7KHVHWULDQJOHVDUHQRWVLPLODU

3. D௘ͽ $VTXDUHDQGDQRQVTXDUHUHFWDQJOHFHUWDLQO\KDYH$$$$EXW
   DUHQRWVLPLODUͼ௘7KHLUVLGHOHQJWKVGRQRWPDWFKLQWKHVDPHUDWLR
   6HHFigure S.10.4௘ͽ
   E௘ͽ $VTXDUHDQGDQRQVTXDUHUKRPEXVKDYH6666EXWDUHQRWVLPLODU
   ͼ௘$QJOHVGRQRWPDWFK6HHFigure S.10.5௘ͽ

x

x

y

y

Figure S.10.1

xxh

a 1 a 2

Figure S.10.2

x x y

y

Figure S.10.3

Figure S.10.4

Figure S.10.5