Question

In the quadrilateral ACBD, AB is a diagonal. If AC = AD and AB bisects $\angle A$, by which congruence property is $\Delta ACB\cong \Delta ADB$?

• A. S.A.S.
• B. A.S.A.
• C. S.S.S.
• D. R.H.S.

Answer 1

The correct option is A S.A.S.

In $\Delta ACB$ and $\Delta ADB$,


AC = AD (Given)
$\angle CAB=\angle DAB\left(ABbisects\angle A\right)$
and AB = AB (Common side)
$\therefore \Delta ACB\cong \Delta ADB$ (S.A.S rule)