Question

In the given figure, if $AD\perp BC$ and BD = DC, then which of the following are true ?

• A. $△BAD\cong △CAD$ by ASA postulate
• B. $△BAD\cong △CAD$ SAS postulate
• C. AD bisects $\angle$ BAC
• D. $△ABC$ is isosceles

Answer 1

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

The correct options are
B $△BAD\cong △CAD$ SAS postulate
C AD bisects $\angle$ BAC
D $△ABC$ is isosceles

In $△BADand△CAD$

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

(ii) $\angle ADB=\angle ADC={90}^{\circ }$

(iii) BD = CD ......(given)

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

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

(vi) AD bisects $\angle BAC$ ........(from (v))

(vii) AB = AC ....(cpct)

(viii) $△ABC$ is isosceles .....(from (vii))

Hence three of the options are correct.