Question

In the given figure, if AB = AD and CB = CD, then which of the following is true ?

• A. $△ABC\cong △ADC$ by SAS postulate
• B. $△ABC\cong △ADC$ by SSS postulate
• C. If $\angle ABC=x^{\circ }$, then $\angle ADC=x^{\circ }$
• D. If $\angle BAC=y^{\circ },$ then $\angle DCA=y^{\circ }$

Answer 1

The correct option is B

$△ABC\cong △ADC$ by SSS postulate

In $△ABC$ and $△ADC$

(i) AB = AD .......(given)

(ii) CB = CD .......(given)

(iii) AC = AC .......(common)

(iv) $△ABC\cong △ADC$ ...... (SSS Postulate)

(v) $\angle ABC=\angle ADC$.....(cpct)

$\therefore$ if $\angle ABC=x^{\circ },$ then $\angle ADC=x^{\circ }$

(vi)$\angle BAC=\angle DAC$....(cpct)

$\therefore$ if $\angle BAC=y^{\circ }$, then $\angle DAC=y^{\circ }$ (and not $\angle DCA=y^{\circ }$)

Hence (B) and (C)