Question

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

• A. $∆ABC\cong ∆DBC$
• B. $∆ABC\cong ∆CBD$
• C. $∆ABC\cong ∆DCB$
• D. $∆ABC\cong ∆BCD$

Answer 1

The correct option is C

$∆ABC\cong ∆DCB$

Explanation for the correct option.

Option $C$ : $∆ABC\cong ∆DCB$

Given: $AB=DC$, $AC=DB$

Common Base is $BC$.

Thus, using $SSS$, $∆ABC\cong ∆DCB$.

Hence, option $C$ is the correct answer.

Explanation for the incorrect option.

Option $A$: $∆ABC\cong ∆DBC$

$AB\ne DB$

Hence, option $A$ is the incorrect answer.

Option $B$: $∆ABC\cong ∆CBD$

$AB\ne CB$

Hence, option $B$ is the incorrect answer.

Option $D$: $∆ABC\cong ∆BCD$

$AB\ne BC$

Hence, option $D$ is the incorrect answer.

Hence, option $C$ is the correct option.