Question

In the given figure, if AB = AC and $\angle ADB=\angle ADC={90}^{\circ }$, then which of the following is true?

• A. $△ABD\cong △ADC$ by RHS postulate
• B. $△ABD\cong △ADC$ by ASA postulate
• C. BD = DC
• D. If $\angle ABD={60}^{\circ },then\angle ACD=30°$

Answer 1

Answer: (A), (C)

The correct options are
A

$△ABD\cong △ADC$ by RHS postulate

C

BD = DC

In $△ABD$ and $△ADC$

(i) $\angle ADB=\angle ADC={90}^{\circ }$ .......(given)

(ii) AD = AD ....... (common)

(iii) AB = AC ....... (given)

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

(v) BD = DC …… (cpct)

(vi) $\angle ABD$ = $\angle ACD={60}^{\circ }$ .......(cpct)

Hence (A) and (C)