Minorand MajorArcs,Semicircle
Asemicircleis half a circle.Amajorarcis longerthan a semicircleand aminorarcis shorterthan a
semicircle.
An arc can be measuredin degreesor in a linearmeasure(cm, ft, etc.).In this lessonwe will concentrate
on degreemeasure.The measureof the minorarc is the sameas the measureof the centralanglethat
correspondsto it. The measureof the majorarc equalsto minusthe measureof the minorarc.
Minorarcs are namedwith two letters—thelettersthat denotethe endpointsof the arc. In the figureabove,
the minorarc correspondingto the centralangle is called. In orderto preventconfusion,
majorarcs are namedwith threeletters—thelettersthat denotethe endpointsof the arc and any otherpoint
on the majorarc. In the figure,the majorarc correspondingto the centralangle is called
.
CongruentArcs
Two arcs that correspondto congruentcentralangleswill also be congruent.In the figurebelow,
becausethey are verticalangles.This also meansthat.Arc AdditionPostulate
The measureof the arc formedby two adjacentarcs is the sum of the measuresof the two arcs.