Question

∆ ABC and ∆ ABD are on a common base AB, and AC = BD and BC = AD as shown in Fig. 18. Which of the following statements is true?
(i) ∆ ABC ≅ ∆ ABD
(ii) ∆ ABC ≅ ∆ ADB
(iii) ∆ ABC ≅ ∆ BAD

Answer 1

In $△$ABC and $△$BAD we have,
AC = BD (given)
BC = AD (given)
and AB = BA (common)
Therefore by SSS criterion of congruency, $△$ABC $\cong$$△$BAD.
There option (iii) is true.