Question

In the given figure, if $\angle BAD=\angle CAD,\angle ABD=\angle ACD,$ then which of the following is false?
a)$△ABD\cong △ACD$ by SAS postulate
b)$△ABD\cong △ACD$ by AAS postulate
c)AB = AC
d)BD = CD

Answer 1

In $△ABD$ and $△ACD$

(i) $\angle ABD=\angle ACD$ ... (given)

(ii) $\angle BAD=\angle CAD$ ... (given)

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

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

(v) AB = AC ... (cpct)

(vi) BD = CD ... (cpct)