Question

decide whether the congruence statement is true. explain your reasoning.
△abd≅△cdb
the congruence statement is
you are given that ab≅
and ad≅
also, bd≅
by the
so, △abd≅
by the
sss congruence theorem.

Explanation:

Step1: Identify corresponding sides

You are given that \( \overline{AB}\cong\overline{CB}\) (marked on the figure as two - tick marks) and \( \overline{AD}\cong\overline{CD}\) (marked on the figure as one - tick mark).

Step2: Use the reflexive property

Also, \( \overline{BD}\cong\overline{DB}\) by the Reflexive Property of Congruence (a segment is congruent to itself).

Step3: Apply SSS Congruence Theorem

So, \( \triangle ABD\cong\triangle CBD\) (the order of the vertices in the congruence statement should match the corresponding sides) by the SSS (Side - Side - Side) Congruence Theorem.

Answer:

The congruence statement \( \triangle ABD\cong\triangle CDB\) is not correct. The correct congruence statement is \( \triangle ABD\cong\triangle CBD\) because \( \overline{AB}\cong\overline{CB}\), \( \overline{AD}\cong\overline{CD}\), and \( \overline{BD}\cong\overline{DB}\) (by the Reflexive Property of Congruence), so by the SSS Congruence Theorem, the triangles are congruent.