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

From the figure, we can see that \(AB\cong CB\), \(AD\cong CD\), and \(BD\cong BD\) (common side).

Step2: Apply SSS Congruence Theorem

Since three pairs of corresponding sides (\(AB = CB\), \(AD = CD\), \(BD=BD\)) are congruent, by the SSS (Side - Side - Side) Congruence Theorem, \(\triangle ABD\cong\triangle CBD\).

Answer:

The congruence statement \(\triangle ABD\cong\triangle CDB\) is true. Because \(AB\cong CB\), \(AD\cong CD\), and \(BD\cong BD\) (common side), so \(\triangle ABD\cong\triangle CBD\) by the SSS Congruence Theorem.