Geometry: An Interactive Journey to Mastery



4. 7ULDQJOHABC has vertices A ͼ௘í௘ͽB ͼ௘௘ͽDQGC ͼ௘௘ͽ)LQGWKHFRRUGLQDWHVRIWKHPLGSRLQW
   M of BCDQGWKHOHQJWKRIWKHOLQHVHJPHQWMA.
   &RPPHQW$OLQHFRQQHFWLQJRQHYHUWH[RIDWULDQJOHWRWKHPLGSRLQWRIWKHRSSRVLWHVLGHLVFDOOHGD
   PHGLDQRIWKHWULDQJOH


5. $SRLQWPLVHTXLGLVWDQWIURPWZRSRLQWVA and B if AP = PB.
   Let A ͼ௘í௘ͽDQGB ͼ௘í௘ͽ
   D௘ͽ 6KRZWKDWWKHSRLQWP ͼ௘௘ͽLVHTXLGLVWDQWIURPA and B.
   E௘ͽ ,VWKHSRLQWQ ͼ௘íí௘ͽHTXLGLVWDQWIURPA and B"
   F௘ͽ ,VWKHSRLQWR ͼ௘íí௘ͽHTXLGLVWDQWIURP A and B"
   G௘ͽ 6KRZWKDWHYHU\SRLQWRIWKHIRUPͼ௘kk௘ͽLVHTXLGLVWDQWIURPA and B.


6. )LQGDSRLQWZLWKyFRRUGLQDWHWKDWLVXQLWVDZD\IURPͼ௘௘ͽ
   &RPPHQW7KHUHDUHWZRSRVVLEOHDQVZHUV&DQ\RX¿QGWKHPERWK"


7. D௘ͽ )LQGDQHTXDWLRQWKDWPXVWEHWUXHIRUWKHQXPEHUVx and yIRUWKHSRLQWA ͼ௘xy௘ͽWRDGLVWDQFH
   RIXQLWVIURPB ͼ௘௘ͽ
   E௘ͽ :KHQ-LQQ\DQVZHUHGWKLVTXHVWLRQVKHFDPHXSZLWKWKHIRUPXODͼ௘xí௘ͽ^2 ͼ௘yí௘ͽ^2  
   ,VVKHFRUUHFW"