Question

In the given figure $AB=BD$ and $\angle BAC=\angle DAC$. Is $△ABC\equiv △ADC$?
If so, state the other pairs of corresponding parts.

Answer 1

In $△ABC$ and $△ADC$, $AC$ is common.
$\angle BAC=\angle DAC$ (Given)
$AB=AD$ (given)
$\therefore △ABC\equiv △ADC$
So, the remaining pairs of corresponding parts are
$BC=DC$, $\angle ABC=\angle ADC,\angle ACB=\angle ACD$ (by c.p.c.t.c)