Geometry: An Interactive Journey to Mastery



FROOLQHDUͼ௘௘ͽ: Two or more points are collinear if they lie on a common line.
FRPSOH[QXPEHUͼ௘௘ͽ$QXPEHURIWKHIRUPa + ib, with a and bHDFKDUHDOQXPEHUDQGi an alleged quantity
with the mathematical property that i^2  í
FRQFDYHSRO\JRQͼ௘௘ͽ$SRO\JRQWKDWLVQRWFRQYH[6HHDOVR convex polygon.
FRQHͼ௘௘ͽ: $¿JXUHLQWKUHHGLPHQVLRQDOVSDFHIRUPHGE\
x GUDZLQJDUHJLRQLQDSODQHͼ௘7KLVZLOOEHFDOOHGWKHEDVHRIWKHFRQH௘ͽ
x selecting a point PDQ\ZKHUHDERYHRUEHORZWKHSODQHͼ௘7KLVZLOOEHFDOOHGWKHFRQHSRLQW௘ͽ
x GUDZLQJDOLQHVHJPHQWIURPHDFKDQGHYHU\SRLQWRQWKHERXQGDU\RIWKHSODQDUUHJLRQWRWKHFKRVHQ
point P.
FRQJUXHQWDQJOHVͼ௘௘ͽ: Two angles of the same measure are congruent.
FRQJUXHQWOLQHVHJPHQWVͼ௘௘ͽ: Two line segments of the same length are congruent.
FRQJUXHQWSRO\JRQVͼ௘௘ͽ: Two polygons that are similar with scale factor k = 1 are congruent. 6HHDOVR
similar polygons.
FRQVWUXFWLEOHQXPEHUͼ௘௘ͽ$UHDOQXPEHUaLVVDLGWREHFRQVWUXFWLEOHLIXVLQJRQO\DVWUDLJKWHGJHͼ௘DUXOHU
ZLWKQRPDUNLQJV௘ͽDQGDFRPSDVVDVWRROVLWLVSRVVLEOHWRGUDZDOLQHVHJPHQWRIOHQJWKa if given only a line
segment of length 1 already drawn on the page.
FRQYH[SRO\JRQͼ௘௘ͽ$SRO\JRQZLWKWKHSURSHUW\WKDWIRUDQ\WZRSRLQWVA and B in the interior of the polygon,
the line segment ABDOVRZKROO\OLHVLQWKHLQWHULRURIWKHSRO\JRQ6HHDOVRconcave polygon.
coordinate planeͼ௘௘ͽSee Cartesian plane/coordinate plane.
FRSODQDUͼ௘௘ͽ: Two or more points are coplanar if they lie on a common plane.
FRVLQHRIDQDQJOHͼ௘LQFLUFOHRPHWU\௘ͽͼ௘௘ͽ$SRLQWPRYHVLQDFRXQWHUFORFNZLVHGLUHFWLRQDORQJDFLUFOHRI
UDGLXV,IWKHDQJOHRIHOHYDWLRQRIWKHSRLQWDERYHWKHSRVLWLYHKRUL]RQWDOD[LVLVx, then the length of the
horizontal displacement, left or right, of the point is denoted cos x and is called the cosine of the angle.
ͼ௘7KHFRVLQHRIDQDQJOHLVGHHPHGQHJDWLYHLIWKHSRLQWLVGLVSODFHGWRWKHOHIW௘ͽ6HHDOVRcosine of an angle
ͼ௘LQWULJRQRPHWU\௘ͽ.