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 = CD
• D. $△ABD\cong △CBD$ by SSS postulate

Answer 1

The correct option is B $△ABD\cong △CBD$ by ASA postulate

In $△ABD$ and $△CBD$,

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

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

(iii) $\angle$ ABD = $\angle$ CBD .... (given, BD bisects $\angle$ ABC)
$\therefore △ABD\cong △CBD$..... (ASA Postulate)

$\Rightarrow$ AB = CB and AD = CD.......(CPCT)