Which missing piece of information would allow the triangles in the figure to be proven congruent by AAS?

The missing piece of information is ∠C ≅ ∠C′
From the figure, we have:
AB ≅ A'B'
<B ≅ <B'
The above means that:
The congruence theorem is given as:
AAS --- Angle Angle Theorem
i.e.
Two corresponding angles and one corresponding side are congruent
Since a congruent side and a congruent angle have been given;
We need a congruent angle to complete the piece
In this case, we have:
∠C ≅ ∠C′
Hence, the missing piece of information is ∠C ≅ ∠C′
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