Geometry: An Interactive Journey to Mastery



Solutions

3. 1RWLFHWKDWl DQGl ZLWKVFDOHIDFWRU%HFDXVHWKHWULDQJOHVVKDUHWKH
   DQJOHEHWZHHQWKHVHVLGHVZHKDYH6$6LQSODFHZLWKk 7KXVw = 8.


4. D௘ͽ alxͼ௘WKHVLGHVEHWZHHQƒDQGƒIRUWKHLUWULDQJOHV௘ͽ
   E௘ͽ bldͼ௘WKHVLGHVEHWZHHQƒDQGƒIRUWKHLUWULDQJOHV௘ͽ
   F௘ͽ dlyͼ௘WKHVLGHVEHWZHHQƒDQGƒIRUWKHLUWULDQJOHV௘ͽ
   G௘ͽ 1R7KHVLGHdLVQRWPDWFKLQJZLWKLWVHOIEHWZHHQWKHWZRWULDQJOHV:HFDQQRWEHVXUHWKDWWKHVFDOH
   factor is 1.


5. The two triangles in Figure S.9.1 share an angle,
   DQGERWKKDYHDƒDQJOH%\$$WKH\DUHVLPLODU

:HKDYH H , giving H  (^36)  feet.

6. 6HHFigure S.9.2.
   The top two triangles are similar by AA.
   ͼ௘%RWKKDYHƒDQGWKH\VKDUHDQDQJOH௘ͽ
   :HKDYH ^6 x, giving x ^1 
   The height of the middle pole is   ^11  feet.


7. D௘ͽ :HKDYHFRQJUXHQWYHUWLFDODQJOHVDQGFRQJUXHQW
   DOWHUQDWHLQWHULRUDQJOHV6RE\$$WKH\DUH
   VLPLODU௘6HHFigure S.9.3௘
   E௘ͽ 7KHVLGHVPDUNHGRIHTXDOOHQJWKDUHQRW
   PDWFKLQJVLGHV:HGRQRWNQRZWKHVFDOHIDFWRU

30 ft

shared angle

80 ft

10 ft

h

Figure S.9.1

12 12 12

5

5

7

7

x^6

Figure S.9.2

Figure S.9.3