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TeachGCSEMaths

UsingCongruence

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Wecanusecongruenttrianglestoprovethatthe

constructionsweusedforbisectinganglesand

lines,anddrawingperpendiculars,actuallydowhat

weclaimed.

Clickbelowtoreviewworkonconstructions:

MoreConstructions:bisectors

Thisishowweconstructedtheperpendicular

bisectorofalinesegment.

C

Theradiiofall4

Narcsareequal.

AB

D

ToprovethatCDistheperpendicularbisector,we

needtoshowthatAN=BN...

andCNA=CNB.

(2equalanglesonastraightlinemusteachbe90.)

C

ToProve:

AN=BN

N

AB

ANC=BNC

D

Proof:WeneedtoprovethattrianglesANCand

BNCarecongruent,buttodothiswefirstneedto

provethattheanglesatCareequal.

IntrianglesACDandBCD,

AC=BCradiiofarcs(S)

AD=BDradiiofarcs(S)

CDiscommon(S)

So,trianglesACDarecongruentand

BCD

C

xxT