Question

$△ABC\text{and}△ABD$ are on a common base AB, and AC = BD and BC = AD as shown in Figure. Which two triangles from $△ABC,△ABD\text{and}△BAD$ are congruent.

Answer 1

$\text{In}△ABC\text{and}△BAD\text{we have,}$
AC = BD (given)
BC = AD (given)
and AB = BA (common)
Therefore by SSS criterion of congruence,
$△ABC\cong △BAD.$