Question

What is the criteria of congruence for $\Delta ABC$ and $\Delta DCB$?

Answer 1

In $\Delta$ABC and $\Delta$DCB,
$\angle ABC=\angle DCB={40}^{\circ }+{30}^{\circ }={70}^{\circ }$
$\angle ACB=\angle DBC={30}^{\circ }$
BC = BC (common side)

$\therefore \Delta ABC\cong \Delta DCB$ by A-S-A criterion.

When two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by A-S-A criterion.