Geometry: An Interactive Journey to Mastery



Lesson 4: Understanding Polygons

Formulas

x 7KHPHDVXUHRIRQHH[WHULRUDQJOHRIDUHJXODUNJRQLVƒN.

x 7KHPHDVXUHVRIDQH[WHULRUDQJOHDQGDQLQWHULRUDQJOHRIDUHJXODUSRO\JRQVXPWRƒ

x $SRO\JRQZLWKNVLGHVVXEGLYLGHVLQWRNíWULDQJOHVZLWKDQJOHVPDWFKLQJWKHLQWHULRUDQJOHVRIWKH

SRO\JRQͼ௘7KXVWKHVXPRIWKHLQWHULRUDQJOHVRIDQNJRQLVͼ௘Ní௘ͽîƒ

Summary

,QWKLVOHVVRQZHSURYHLQÀDWJHRPHWU\WKDWWKHH[WHULRUDQJOHVRIDFRQYH[SRO\JRQDUHVXUHWRVXPWRƒ

LUUHVSHFWLYHRIWKHQXPEHURIVLGHVWKDWWKHSRO\JRQKDV7KLVSURYLGHVDVLPSOHPHDQVWRFRPSXWHWKHPHDVXUHV

RIWKHH[WHULRUDQGLQWHULRUDQJOHVRIUHJXODUSRO\JRQV7KLVKDVDSSOLFDWLRQVWRWLOLQJWKHSODQHZLWKUHJXODU

SRO\JRQV

Example 1

)LQGWKHPHDVXUHRIWKHLQWHULRUDQJOHRIDUHJXODUSHQWDJRQ

Solution

7KH¿YHH[WHULRUDQJOHVRIWKHUHJXODUSHQWDJRQVXPWRƒDQGKDYHWKHVDPHPHDVXUH

7KXVHDFKH[WHULRUDQJOHKDVPHDVXUHƒ ƒ&RQVHTXHQWO\HDFKLQWHULRUDQJOHKDVPHDVXUHƒ

Example 2

$UHJXODUSRO\JRQKDVLQWHULRUDQJOHƒ+RZPDQ\VLGHVGRHVWKHSRO\JRQKDYH"

Solution

(DFKH[WHULRUDQJOHRIWKHUHJXODUSRO\JRQKDVPHDVXUHƒ

,INLVWKHQXPEHURIVLGHVRIWKHSRO\JRQWKHQƒN ƒ so N 

Example 3

ABCDEFGHIJKLLVDUHJXODUGRGHFDJRQ6HJPHQWVAB and CDDUHH[WHQGHGWRPHHWDWDSRLQWM. Find the

PHDVXUHRI‘BMC.