Perpendiculars and Bisectors

Perpendicular Bisector:

A segment, ray, line or plane that is perpendicular to a

segment at its midpoint.

endpoint

CA CB

equidistant

DA DB

Inthediagramshown,𝑀𝑁 !⃖!!!!!⃗ istheperpendicularbisectorof𝑆𝑇!!!!a.Whatsegmentlengthsinthediagramareequal?NS=NT(Because𝑀𝑁 !⃖!!!!!!⃗ bisects𝑆𝑇!!!!)MS=MT(PerpendicularBisectorTheorem)QS=QT(Thediagramshowsthis)b.ExplainwhyQison𝑀𝑁 !⃖!!!!!!⃗ QS=QT,soQisequidistantfromSandT.Becauseoftheconverseoftheperpendicularbisectortheorem,Qisontheperpendicularbisectorof𝑆𝑇!!!!,whichis𝑀𝑁

sides

CADBAD

sides

DB DC

Congruent

Congruent

Equal

False

𝑚 < 1 = 55°,𝑚 < 2 = 55°, 𝑚 < 3 = 20°,𝑚 < 4 = 70°,𝑚 < 5 = 35°,

𝑚 < 6 = 50°,