Geometry: An Interactive Journey to Mastery

(Greg DeLong) #1


/HVVRQ%HJLQQLQJV²-DUJRQDQG8QGH¿QHG7HUPV


x straight angle: $QDQJOHZLWKPHDVXUHƒLVDVWUDLJKWDQJOH
x vertical angles7ZRDQJOHVRQRSSRVLWHVLGHVRIWKHSRLQWRILQWHUVHFWLRQRIWZRLQWHUVHFWLQJOLQHVDUH
YHUWLFDODQJOHV
Notation
x 3RLQWVDUHODEHOHGZLWKFDSLWDOOHWWHUV
x $OLQHWKURXJKSRLQWVA and B is denoted ABHJJG.
x 7KHOLQHVHJPHQWFRQQHFWLQJSRLQWVA and B is denoted AB.
x 7KHOHQJWKRIWKHOLQHVHJPHQWAB is denoted AB.
x &RQJUXHQWOLQHVHJPHQWVDUHGHQRWHGAB#CD.2QGLDJUDPVFRQJUXHQWOLQHVHJPHQWVDUHJLYHQWKH
VDPHPDUNLQJV
x 7KHDQJOHJLYHQE\WZROLQHVHJPHQWVPQ and QR is denoted ‘PQR or ‘RQP.8QOHVVWROG
RWKHUZLVHRQHLVWRDVVXPHWKDWWKLVUHIHUVWRWKHDQJOHRIVPDOOHUPHDVXUH
x &RQJUXHQWDQJOHVDUHGHQRWHG‘#‘PQR ABC.2QGLDJUDPVFRQJUXHQWDQJOHVDUHJLYHQPDWFKLQJ
ODEHOV
x 3HUSHQGLFXODUOLQHVRUOLQHVHJPHQWVDUHGHQRWHGABACD.
Result
x YHUWLFDODQJOHWKHRUHP 9HUWLFDODQJOHVDUHFRQJUXHQW
Summary
*HRPHWU\LVWKHVWXG\RISRLQWVOLQHVͼ௘FXUYHGDQGVWUDLJKW௘ͽDQGVXUIDFHVDQGWKH¿JXUHVRQHFDQFRQVWUXFWZLWK
WKHP$VZHVHHLQWKLVOHVVRQLWLVQRWSRVVLEOHWRGH¿QHH[DFWO\ZKDWZHPHDQE\³SRLQW ́³OLQH ́RU³VWUDLJKW ́
IRUH[DPSOHHYHQWKRXJKZHIHHOWKDWZHKDYHDJRRGLQWXLWLYHXQGHUVWDQGLQJRIZKDWWKHVHFRQFHSWVPHDQ
:HEHJLQWKLVOHVVRQUHO\LQJRQRXULQWXLWLRQWRHVWDEOLVKWKHQRWDWLRQDQGODQJXDJHWKDWLVQRZVWDQGDUGLQWKH
VWXG\RIJHRPHWU\7KHSKLORVRSKLFDOFRQFHUQVRISLQQLQJGRZQZKDWWKHVHEHJLQQLQJWHUPVPHDQOHDGXVWRWKH
SUREOHPRIFLUFXODUUHDVRQLQJDQGWKHQHHGIRUVHWWLQJXQGH¿QHGWHUPVFRXSOHGZLWKSRVWXODWHV
:LWKSKLORVRSKLFDOGLI¿FXOWLHVLQFKHFNZHHQGWKHOHVVRQZLWKWKHODQJXDJHDQGQRWDWLRQRIDQJOHV
Free download pdf