Question

In the given figure if AB = AC and AD bisects $\angle BAC$, then which of the following are true ?

• A. $△BAD\cong △CAD$ by ASA postulate
• B. $△BAD\cong △CAD$ by SAS postulate
• C. $AD\perp BC$
• D. D is the mid point of BC

Answer 1

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

The correct options are
B

$△BAD\cong △CAD$ by SAS postulate

C

$AD\perp BC$

D

D is the mid point of BC

In $△BAD$ and $△CAD$

(i) AD = AD ......(common)

(ii) $\angle DAB=\angle CAD$.....(given AD bisects $\angle$ BAC)

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

(iv)$△BAD\cong △CAD$ ....(SAS postulate)

(v) $\angle ADB=\angle ADC=x^{\circ }$ (say)......(cpct)

(vi)$2x^{\circ }={180}^{\circ }....\left(\angle ADBand\angle ADClieinastraightline\right)$

$x={90}^{\circ }$

$\therefore AD\perp BC$

(vii) BD = DC .......(cpct)

(viii) D is the midpoint of BC......(from (vii))

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