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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
Solution
∆ABC ≅ ∆DCB
Explanation:
In ∆ABC and ∆DCB,
AB = DC ......(Given)
AC = DB ......(Given)
BC = CB ......(Common)
∴ ∆ABC ≅ ∆DCB ......(SSS criterion)
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