In the following figure, $△ A B C ≅ △ A C D$ if ___.

BC = AC

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BC = AD

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CD = AC

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BC = CD

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Solution

The correct option is D
BC = CD

Given, in $△ A B C$ and $△ A D C$ ,
AB = AC
AC = AD

We see that two sides of one triangle are equal to the two sides of another triangle. If the remaining sides also become equal, then the two triangles considered will become congruent.

So, if BC = CD, then by SSS rule of congruence, $△ A B C$ will be congruent to $△ A C D$ .

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