Question

Question 49

If $\Delta ABC$ and $\Delta DBC$ are on the same base BC, AB = DC and AC = DB as shown in the figure, then which of the following gives a congruence relationship?

a) $\Delta ABC\cong \Delta DBC$
b) $\Delta ABC\cong \Delta CBD$
c) $\Delta ABC\cong \Delta DCB$
d) $\Delta ABC\cong \Delta BCD$

Answer 1

Since, AB = DC [given]
and AC = DB
BC = BC [common base]
$\therefore$ By SSS congruence criterion,
$\Delta ABC\cong \Delta DCB$