Question

In the given figure, if $AB=AD$ and $CB=CD$, then

• A. $△$ $ABC$ $\cong$ $△$ $ADC$
• B. $\angle$ $BCA=$ $\angle$ $DCA$
• C. $\angle$ $ADC=$ $\angle$ $ABC$
• D. All of these

Answer 1

Answer: (D)

All of these

In $△$ $ABC$ and $△$ $ADC$, we have
$AB=AD$ (given)
$CB=CD$ (given)
$AC=AC$ (common)
$\therefore$ $△$ $ABC$ $\cong$ $△$ $ADC$ (By SSS)
$\therefore$ $\angle$ $ADC=$ $\angle$ $ABC$ and $\angle$ $BCA=$ $\angle$ $DCA$ (By CPCT)