Geometry: An Interactive Journey to Mastery

Example 2
:KDWLVWKHPLVVLQJOHQJWKLQWKHWULDQJOHWKDWLV
LQFKHVKLJK"
ͼ௘$VVXPHWKDWWKHKHLJKWRIWKHWULDQJOHLVPHDVXUHG
IURPWKHEDVHRIWKHWULDQJOHWRWKHDSH[RIWKHWULDQJOH
DWDQDQJOHRIƒ6HHFigure 5.2௘ͽ
:DUQLQJ7KLVWULDQJOHLVnotDULJKWWULDQJOH
Solution
8VLQJ3\WKDJRUDV¶VWKHRUHPWZLFHZHVHHWKDWWKH
PLVVLQJVLGHOHQJWKLV        
ͼ௘7KLVGRHVQRWHTXDO  See Figure 5.3௘ͽ
Example 3
:KLFKORFDWLRQIRUWKHSRLQWPLQVLGHDVTXDUHJLYHVWKHVPDOOHVWYDOXH
IRUWKHVXPRIWKHGLVWDQFHVabcdVKRZQ":K\"
ͼ௘6HHFigure 5.4௘ͽ
Solution
3ODFLQJWKHSRLQWPDWWKHFHQWHURIWKHVTXDUHJLYHV
DVXPabcdWKDWLVVPDOOHVWͼ௘6HHFigure 5.5௘ͽ
+HUHWKHVXPHTXDOVWZLFHWKHOHQJWKRIWKHGLDJRQDORIWKHVTXDUH
3ODFLQJPDWDQ\RWKHUORFDWLRQJLYHVDVXPWKDWLVJUHDWHUWKDQWKLV
7RVHHZK\VXSSRVHWKDWPLVSODFHGRIIFHQWHUͼ௘6HHFigure 5.6௘ͽ
7KHWULDQJXODULQHTXDOLW\VKRZVWKDWWKHVXPbdLVORQJHUWKDQ
WKHGLDJRQDORIWKHVTXDUH
,QWKHVDPHZD\WKHVXPacLVORQJHUWKDQWKHGLDJRQDORIWKHVTXDUH
&RQVHTXHQWO\abcdLVORQJHUWKDQWKHWZRGLDJRQDOVRIWKHVTXDUH

(^942)
Figure 5.2
(^942)
Figure 5.3
a
bc
d
p
Figure 5.4
a
bc
d
p
Figure 5.5
a
bc
d
p
Figure 5.6