Geometry: An Interactive Journey to Mastery



7KHGLVWDQFHEHWZHHQ©¹§· ̈ ̧ 22  and   is

^2222 

MB   § · § · §· §· ̈ ̧ ̈ ̧ ̈ ̧ ̈ ̧© ¹ © ¹ ©¹ ©¹

These distances are indeed the same.
$OVRAB   ^22  so AMMBGRHVHTXDOAB.
Example 3
6XSSRVHWKDWP ͼ௘km௘ͽDQGR ͼ௘kím௘ͽ)LQGWKHFRRUGLQDWHVRIDSRLQWS so that RLVWKHPLGSRLQWRIPS.
Solution
:HQHHGDSRLQWS ͼ௘ab௘ͽZLWK
kWKHPLGGOHYDOXHEHWZHHQk and a
and
ímWKHPLGGOHYDOXHEHWZHHQm and b.
&DQ\RXVHHWKDWa kGRHVWKHWULFNIRUa"ͼ௘,W¶VDQRWKHU³kXS ́IURPk௘ͽ
&DQ\RXVHHWKDWb ímZRUNV"ͼ௘,W¶VDQRWKHU³mGRZQ ́IURPím௘ͽ
:HKDYHS ͼ௘kím௘ͽ
Study Tips
x 5HPHPEHUWKDWWKHGLVWDQFHIRUPXODLVMXVWWKH3\WKDJRUHDQWKHRUHP:RUNWRVHHWKHSLFWXUHRIDULJKW
WULDQJOHLQWKHFRRUGLQDWHSODQHLQ\RXUPLQGͼ௘RURQSDSHU௘ͽUDWKHUWKDQPHPRUL]HDIRUPXOD
x .HHSLQPLQGWKDWWKHPLGSRLQWRIDOLQHVHJPHQWAB has xFRRUGLQDWHWKHPLGGOHYDOXHRIWKH
xFRRUGLQDWHVRIA and B and yFRRUGLQDWHWKHPLGGOHYDOXHRIWKHyFRRUGLQDWHVRIA and Bͼ௘7KLVIHHOV
QDWXUDODQGULJKWDQGPRUHRYHULVPDWKHPDWLFDOO\FRUUHFW௘ͽ