Question

plz help
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Answer 1

$\underline{\sf\ \ \ Given:-\ \ }$

∆ADC and ∆ABC

AZ is bisector of $\sf\ \angle DAB\ and \angle DCB$

$\underline{\sf\bigstar\ \ To\ Prove :-\ \ }\begin{cases}\sf{\Delta BAC \cong \Delta DAC}\\ \sf{AB=AD}\\ \sf{CD=CB}\end{cases}$

$\underline{\underline{\sf\bigstar\ Proof :-}}$

$\sf\ \ In \ \Delta ADC\ and \Delta ABC\\ \\ \\ :\implies\sf \angle DAC= \angle BAC\ \ \ \ \ \big\lgroup AZ\ Bisector \big\rgroup\\ \\ \\ :\implies\sf \angle DCA= \angle BCA\ \ \ \ \ \big\lgroup Bisector \big\rgroup\\ \\ \\ :\implies\sf AC= AC\ \ \ \ \ \big\lgroup\ Common \big\rgroup\\ \\ \\ :\implies\sf \ \Delta ADC \cong \Delta ABC\ \ \ \ \ \big\lgroup\ By\ ASA\ Criteria \big\rgroup$

$\bullet\sf \ \ AB= AD\ \ \ \ \big(CPCT\big)\\ \\ \\ \bullet\sf\ \ CB=CD\ \ \ \ \ \big(CPCT\big)$