Anglesand Transversals
Manymathproblemsinvolvethe intersectionof threeor morelines.Examinethe diagrambelow.
In the diagram,lines and are crossedby line. We havequitea bit of vocabularyto describethis
situation:
- Line is calledatransversalbecauseit intersectstwo otherlines ( and ). The intersectionof line
with and formseightanglesas shown.- The area betweenlines and is calledtheinteriorof the two lines. The area not betweenlines
and is calledtheexterior.- Angles and are calledadjacentanglesbecausethey sharea side and do not overlap.There
are manypairsof adjacentanglesin this diagram,including and , and , and and
.- and areverticalangles.Theyare nonadjacentanglesmadeby the intersectionof two lines.
Otherpairsof verticalanglesin this diagramare and , and , and and.- Correspondinganglesare in the samepositionrelativeto both linescrossedby the transversal.
is on the upperleft cornerof the intersectionof lines and. is on the upperleft cornerof the in-
tersectionof lines and. So we say that and are correspondingangles.- and are calledalternateinteriorangles.Theyare in the interiorregionof the lines and
and are on oppositesidesof the transversal.- Similarly, and arealternateexterioranglesbecausetheyare on oppositesidesof the
transversal,and in the exteriorof the regionbetween and.- Finally, and areconsecutiveinteriorangles.Theyare on the interiorof the regionbetween
lines and and are next to eachother. and are also consecutiveinteriorangles.