Question

In the given figure, if AB = CD and D is the midpoint of BC, then which of the following is true ?

• A. $△ADB\cong △ADC$ by RHS postulate
• B. $△ADB\cong △ADC$ by SSS postulate
• C. AD bisects $\angle BAC$
• D. If $\angle BAC={80}^{\circ },$ then $\angle ABD={80}^{\circ }$

Answer 1

Answer: (B), (C)

The correct options are
B

$△ADB\cong △ADC$ by SSS postulate

C

AD bisects $\angle BAC$

In $△ABD$ and $△ACD$

(i) AB = AC .........(given)

(ii) BD = CD .........(given)

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

(iv)$△ABD\cong △ACD$ ......(SSS Postulate)

(v) $\angle BAD=\angle CAD$ .....(cpct)

$\therefore$ AD bisects $\angle$ BAC

(vi) $\angle ABD=\angle ACD$ .....(cpct)

If $\angle BAC={80}^{\circ }$, then $\angle ABD=\angle ACD={50}^{\circ }$ (and not ${80}^{\circ }$)

Hence (B) and (C)