Geometry: An Interactive Journey to Mastery



Formulas

Polygons
$SRO\JRQZLWKNVLGHVVXEGLYLGHVLQWRNíWULDQJOHVZLWKDQJOHVPDWFKLQJWKHLQWHULRUDQJOHVRIWKH
SRO\JRQͼ௘7KXVWKHVXPRIWKHLQWHULRUDQJOHVRIDQNJRQLVͼ௘Ní௘ͽîƒ

Regular Polygons
7KHPHDVXUHRIRQHH[WHULRUDQJOHRIDUHJXODUN-gon is ƒN.
7KHPHDVXUHVRIDQH[WHULRUDQJOHDQGDQLQWHULRUDQJOHRIDUHJXODUSRO\JRQVXPWRƒ

Distance and Midpoints
7KHGLVWDQFHEHWZHHQWZRSRLQWVLQWKHSODQHWKDWKDYHEHHQDVVLJQHGFRRUGLQDWHVLV
distance  difference in -valuesxy^22 difference in -values.

The midpoint of the line segment connecting P ͼ௘x 1 , y 1 ௘ͽDQGQ ͼ௘x 2 , y 2 ௘ͽLVM (^) ©¹ ̈ ̧§·xx^12  22 ,.yy^12 
Lines
$OLQHRIVORSH mWKURXJKWKHSRLQWͼ௘a, b௘ͽKDVHTXDWLRQyíb = mͼ௘xía௘ͽͼ௘2IFRXUVHWKHUHDUHPDQ\
DOJHEUDLFDOO\HTXLYDOHQWYHUVLRQVRIWKLVHTXDWLRQ௘ͽ
3DUDOOHOOLQHVKDYHWKHVDPHVORSH
If one line has slope m, then a line perpendicular to it has slope m^1 .ͼ௘DVVXPLQJWKDWQHLWKHUOLQH
LVYHUWLFDO௘ͽ
Area
area of a rectangle: length × width.
area of a triangle:^12 EDVHîKHLJKWͼ௘7KLVIRUPXODDSSOLHVQRPDWWHUZKLFKVLGHLVFRQVLGHUHGWKHEDVH௘ͽ