Geometry: An Interactive Journey to Mastery



/HVVRQ%HJLQQLQJV²-DUJRQDQG8QGH¿QHG7HUPV

Example 3

7ZRDQJOHVDUHFRPSOHPHQWDU\LIWKHLUPHDVXUHVVXPWRƒDQGVXSSOHPHQWDU\ LIWKHLUPHDVXUHVVXPWRƒ

,IWKHFRPSOHPHQWRIDQDQJOHLVƒZKDWLVLWVVXSSOHPHQW"

Solution

7KHDQJOHLQTXHVWLRQKDVPHDVXUHƒͼ௘EHFDXVH ௘ͽ,WVVXSSOHPHQWLVWKXVƒíƒ ƒ

Study Tip

x 2YHUWKHODVWWZRPLOOHQQLDDJUHDWGHDORIMDUJRQKDVEHHQGHYHORSHGDQGXVHGLQWKHVWXG\DQG

SUDFWLFHRIJHRPHWU\PDQ\PRUHZRUGVDQGQDPHVWKDQKDYHEHHQSUHVHQWHGLQWKLVOHVVRQ%HVXUHWR

XQGHUVWDQGWKHGH¿QLWLRQVRIDQ\QHZZRUGV\RXHQFRXQWHU

Pitfall

x 'LDJUDPVLQJHRPHWU\QHHGQRWEHGUDZQDFFXUDWHO\'RQRWDVVXPHIRUH[DPSOHWKDWDQDQJOHLQD

GLDJUDPLVDULJKWDQJOHHYHQLILWDSSHDUVWREHRQH5HO\RQO\RQWKHLQIRUPDWLRQH[SOLFLWO\VWDWHGLQD

TXHVWLRQRUH[SOLFLWO\PDUNHGRQDGLDJUDP

1. ,QWKHGLDJUDPLQFigure 2.3PQ and SRHJG intersect at OZKLFKLVDOVRWKHPLGSRLQWRIPQ.
   ,VHDFKRIWKHIROORZLQJVWDWHPHQWVWUXHRUIDOVH"
   D௘ͽ PO#OQ.
   E௘ͽ PSDQGR are collinear.
   F௘ͽ PRDQGQDUHFRSODQDU
   G௘ͽ PO = QO.
   H௘ͽ POLVFRQJUXHQWWRQO.
   I௘ͽ POOQ = PQ.

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Figure 2.

Problems