Question

In the given figure $\angle$ ADB = $\angle$ CDB. If BD bisects $\angle$ ABC, then which of the following is true ?

• A. $△ABD\cong △CBD$ by SAS postulate
• B. $△ABD\cong △CBD$ by ASA postulate
• C. AB = BC
• D. AD = CD

Answer 1

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

The correct options are
B

$△ABD\cong △CBD$ by ASA postulate

C

AB = BC

D

AD = CD

In $△ABD$ and $△CBD$,

(i) $\angle$ ADB = $\angle$ CDB .... (given)

(ii) DB = DB .... (common)

(iii) $\angle$ ABD = $\angle$ CBD .... (given, BD bisects $\angle$ ABC)

(iv) $△ABD\cong △CBD$..... (ASA Postulate)

(v) AB = CB .......(cpct)

(vi) AD = CD.......(cpct)

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