IntersectingPerpendicularLines
We can extendwhat we just said aboutlinearpairsto all pairsof congruentsupplementaryangles:Congruent
supplementaryangleswill alwaysmeasure each.Whenyou haveperpendicularlines,however, four
differentanglesare formed.
Thinkaboutwhatyou just learned.If two anglesare a linearpair, and one of themmeasures the other
will also measure Fill in the measuresof and in the diagramto showthat they are both right
angles.
Now thinkbackto whatyou learnedearlierin this chapter. Verticalanglesare two angleson oppositesides
of intersectinglines.Applyingthe VerticalAnglesTheorem,we knowthat verticalanglesare also congruent.
Usingthis logic you can provethat all four of the anglesin this diagramare right angles.
Now that you knowhow to identifyright anglesformedby perpendicularlines,you can use this theoremfor
manydifferentapplications.Alwaysbe on the lookoutfor angleswhosemeasuresyou knowbecauseof
perpendicularlines.