In the diagram, AB = DC and AC = DB. The line BD intersect the line AC at T.

1. Identify the three pairs of equal corresponding sides.

In $\triangle ABC$ and $\triangle DCB$,

$AB = DC$ given,

$AC = DB$ given,

$BC = CB$ common side.

2. State the congruence conclusion with the correct test.

Since all three corresponding sides are equal,

$\triangle ABC \cong \triangle DCB$ by SSS.

1. Use congruence from part (a) to identify equal corresponding angles and relate them to triangle $TBC$.

From part (a), $\triangle ABC \cong \triangle DCB$.

Therefore corresponding angles are equal:

$\angle ACB = \angle DBC$.

Since $T$ lies on $AC$ and $DB$,

$\angle TCB = \angle TBC$.

Hence $TB = TC$, so $\triangle TBC$ is isosceles.