Fast!!!2 maths question

2010-09-15 7:25 am

1.In the figure one ,CD is a diameter of the circle , centre O.Prove that
AP=OQ and OP=BQ.2.ln the figure two ,Triangle PQR and Triangle RTS are equliateral triangles.(a)Prove that PS=QT.
(b)IF PS is produced to cut QT at U.find angle QUS.

圖片參考：http://imgcld.yimg.com/8/n/HA00543461/o/701009140161313873371160.jpg

回答 (1)

用戶2053

2010-09-15 8:41 am

✔ 最佳答案

1) OA = OB = radiusㄥAOP = 180° - 90° - ㄥBOQ = 90° - ㄥBOQ = ㄥOBQㄥAPO = ㄥOQB = 90° (Given)△OAP =~= △BOQ (A.S.A.)So AP=OQ and OP=BQ.
2a)PR = QR , (Sides of equliateral triangles PQR)RS = RT , (Sides of equliateral triangles RST)ㄥPRS = ㄥQRT = 60° , (a inter - angle of equliateral triangles)△PSR =~= △QTRSo PS = QT2b)ㄥRQU = ㄥRTS since △PSR =~= △QTR ,ㄥQSU = ㄥPSR (對頂角)△PSR ~ △QSU (A.A.)So ㄥQUS = ㄥPRS = 60°

2010-09-15 00:44:50 補充：
2a)

△PSR =~= △QTR (S.A.S.)

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