Discussion
A and D are two points lying on the same side of line segment BC, such that AB = 5 cm, AC = 8 cm, BC = 4 cm, BD = 8 cm and CD = 5 cm. Then,
Answer: B
The correct statement is \(\Delta ABC \cong \Delta DCB\), by SSS.
Match the sides: AB = 5 = DC, BC = 4 = CB and AC = 8 = DB. All three pairs of sides are equal, so the triangles are congruent by SSS, with the correspondence A ↔ D, B ↔ C and C ↔ B.
Writing \(\Delta DBC\) would pair AB with DB (5 with 8), which is wrong, so the order of letters matters. SAS is not the reason, since no angle is given; the congruence comes from the three sides alone.
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