Geometry: An Interactive Journey to Mastery

5. Label x, the length of the diagonal at the base of the cube, as shown
   in Figure S.5.5.
   %\WKH3\WKDJRUHDQWKHRUHPIRUWKHWULDQJOHRQWKHERWWRPIDFH
   1  + 1 = x, giving x 
   %\WKH3\WKDJRUHDQWKHRUHPIRUWKHVKDGHGWULDQJOHx + 1 = d.
   7KXV d, giving d 3.


6. /DEHODVVXJJHVWHGE\WKHKLQW௘6HHFigure S.5.6௘
   :HKDYHWKHIROORZLQJ
    
   xh  xh  
   ([SDQGWKHVHFRQGHTXDWLRQ
    xxxh 
   0DNHXVHRIWKH¿UVWHTXDWLRQ
      
    
   

xx

x

x



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64

8.

h

h

h

h





7. D௘ͽ ,PSRVVLEOH7ZRVLGHVFDQQRWDGGWROHVVWKDQWKHWKLUGVLGH
   E௘ͽ ,PSRVVLEOH7ZRVLGHVFDQQRWDGGWROHVV
   than the third side.
   F௘ͽ 3RVVLEOH)RUH[DPSOHZHKDYHWKHULJKW
   triangle shown in Figure S.5.7.

Q

P

1

1

(^1) x
d
Figure S.5.5
x íx
h
APC

B

17 10

Figure S.5.6

1 160, 001 400

Figure S.5.7