in the given figure, AC=AE,AB=AD and <BAD=<EAC. show that BC=DE
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ANSWER :
GIVEN : AC=AE & AB=AD & ANGLE BAD = ANGLE EAC
TO PROOF : BC = DE
CONSTRUCTION : JOIN PT. D AND PT. E TO CONSTRUCT LINE SEGMENT DE
PROOF : AS ANGLE BAD = ANGLE EAS AND AS DAC IS AN ANGLE BETWEEN THEM
THEREFORE, ANGLE BAC = ANGLE EAD - 1
IN ∆BAC AND ∆EAD BY CONGRUENCE
AB = AD (GIVEN)
ANGLE BAC = ANGLE EAD (FROM 1)
AC = AE (GIVEN)
THEREFORE, ∆BAC ≈ ∆EAD BY SAS CONGRUENCE RULE
THEREFORE, BY CPCT BC = DE
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