Question

If ∆ABC and ∆DBC are on the same base BC, AB = DC and AC = DB (see figure), then which of the following gives a congruence relationship?

Options

• ∆ABC ≅ ∆DBC

• ∆ABC ≅ ∆CBD

• ∆ABC ≅ ∆DCB

• ∆ABC ≅ ∆BCD

Answer 1

∆ABC ≅ ∆DCB

Explanation:

In ∆ABC and ∆DCB,

AB = DC  ...(Given)

AC = DB  ...(Given)

BC = CB  ...(Common)

∴ ∆ABC ≅ ∆DCB  ...(SSS criterion)