question_answer

In quadrilateral\[ACBD\], \[AB\] is a diagonal. If \[AC=AD\] and \[AB\] bisects\[\angle A\], by which congruence property is?

A)  S.A.S.   

B)                     A.S.A. 

C)         S.S.S.             

D)         R.H.S.             

Correct Answer: A

Solution :

In \[\Delta ACB\]and \[\Delta ADB,AC=AD\](Given) \[\angle CAB=\angle DAB\](AB bisects\[\angle A\]) and \[AB=AB\](Common side) \[\therefore \]\[\Delta ACB\cong \Delta ADB\](S.A.S. rule)