In the figure, DB is a shared side of triangles ADB and CDB. It is given that DA ≅ DC and AB ≅ CB. Which postulate or theorem proves △ADB ≅ △CDB, and what is the role of DB in the proof?
AASA (Angle-Side-Angle) — DB serves as the included side between two pairs of congruent angles
BHL (Hypotenuse-Leg) — this only applies here if the triangles are known to be right triangles, which is not given
CSAS (Side-Angle-Side) — DB is the included angle's vertex, so an angle pair must also be marked congruent
DSSS (Side-Side-Side) — DB ≅ DB by the Reflexive Property, giving three pairs of congruent sides
Explanation
Two sides are given congruent (DA≅DC, AB≅CB), and the shared side DB is congruent to itself by the Reflexive Property (DB ≅ DB). That's three pairs of congruent corresponding sides with no angle information given, so SSS applies.
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