Geometry: An Interactive Journey to Mastery

Solutions

5. D௘ͽ 1R ^103 LVQRWJUHDWHUWKDQ
   E௘ͽ :HQHHGx!ͼ௘WKDWLVx!௘ͽDQGx!ͼ௘DOUHDG\WUXH௘ͽ
   DQG!xͼ௘WKDWLVx௘ͽ
    7KXVx௘6HHFigure S.15.3௘
   F௘ͽ :HKDYHd^2  x^2 ^2 6Rd^2 !^2 JLYLQJd!7KDWLVDERXW
   DOOZHFDQVD\௘6HHFigure S.15.4௘
   G௘ͽ :HQHHGab!xDQGxa!bͼ௘JLYLQJx!bía௘ͽ
   DQGxb!aͼ௘DXWRPDWLFDOO\WUXHEHFDXVHbLVODUJHUWKDQa௘ͽ
    3XWWLQJWKHVHWRJHWKHUJLYHV bíaxba௘6HHFigure S.15.5௘


6. D௘ͽ $OZD\V%HFDXVHWKHDQJOHVLQDWULDQJOHVXPWRƒWKHWZRFRQJUXHQWEDVH
   DQJOHVPXVWHDFKKDYHPHDVXUHOHVVWKDQƒ
   E௘ͽ 6RPHWLPHV)RUH[DPSOHFRQVLGHUFigure S.15.6
   F௘ͽ 6RPHWLPHV&RQVLGHUFigure S.15.7


7. $QJOHx ƒ1RZyz ƒZLWKzODUJHUWKDQyEHFDXVHLWLV
   RSSRVLWHDORQJHUVLGHWKDQyͼ௘:HSURYHGWKLVJHQHUDOSURSHUW\LQWKH
   OHVVRQ௘ͽ7KLVPHDQVWKDWzLVODUJHUWKDQƒDQGyLVVPDOOHUWKDQƒ
   :HKDYHyxz


8. %\WKHWULDQJXODULQHTXDOLW\ABBC!ACDQGADDC!AC
   1RZDGGWRJHWABBCADDC!ͼ௘AC௘ͽ


9. L UHHS!USEHFDXVHRIWKHWULDQJOHLQHTXDOLW\
   LL US!TSEHFDXVH‘!‘TTUS
   LLLUHHS!TSEHFDXVHRIDOJHEUD

x

6

7

Figure S.15.3

x d

50

Figure S.15.4

a b

x

Figure S.15.5

Figure S.15.6

Figure S.15.7