Answer :

Given: BAD = DAC


To prove: AB>BD and AC>DC


Proof:


In ∆ACD,


ADB = DAC + ACD … exterior angle theorem


= BAD + ACD … given that BAD = DAC


ADB > BAD


The side opposite to angle ADB is the longest side in ADB


So, AB > BD


Similarly in ∆ABD


ADC = ABD + BAD … exterior angle theorem


= ABD + CAD … given that BAD = DAC


ADC > CAD


The side opposite to angle ADC is the longest side in ACD


So, AC > DC


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