Question

In the given figure, if $\angle BAD=\angle CAD,\angle ABD=\angle ACD,$ then which of the following is true ?

• A. $△ABD\cong △ACD$ by SAA postulate
• B. $△ABD\cong △ACD$ by AAS postulate
• C. AB = AC
• D. BD = CD

Answer 1

Answer: (B), (C), (D)

The correct options are
B

$△ABD\cong △ACD$ by AAS postulate

C

AB = AC

D

BD = CD

In $△ABD$ and $△ACD$

(i) $\angle ABD=\angle ACD$ ........(given)

(ii) $\angle BAD=\angle CAD$ .....(given)

(iii) AD = AD ............(common)

(iv) $△ABD\cong △ADC$ ........(AAS Postulate)

(v) AB = AC ......(cpct)

(vi) BD = CD .......(cpct)

Hence (B), (C) and (D)