Question

decide whether the congruence statement is true. explain your reasoning.
$\triangle abd \cong \triangle cdb$
the congruence statement is \boxed{} you are given that $\overline{ab} \cong$ \boxed{} and $\overline{ad} \cong$ \boxed{} also, $\overline{bd} \cong$ \boxed{} by
the \boxed{} so, $\triangle abd \cong$ \boxed{} by the sss congruence theorem.
options:
$\overline{db}$, $\overline{cd}$, $\overline{cb}$, correct, not correct, $\triangle cbd$, $\triangle bcd$, $\triangle cdb$, $\triangle dcb$, $\triangle dbc$, $\triangle bdc$, symmetric property of congruence, reflexive property of congruence, transitive property of congruence

Explanation:

Step1: Identify congruent sides

From the diagram: $\overline{AB} \cong \overline{CD}$, $\overline{AD} \cong \overline{CB}$

Step2: Identify shared side property

$\overline{BD} \cong \overline{DB}$ by Reflexive Property of Congruence

Step3: Apply SSS Congruence Theorem

Three pairs of corresponding sides are congruent, so $\triangle ABD \cong \triangle CDB$

Step4: Verify statement validity

The given congruence statement matches the result, so it is correct.

Answer:

The congruence statement is correct
You are given that $\overline{AB} \cong \boldsymbol{\overline{CD}}$ and $\overline{AD} \cong \boldsymbol{\overline{CB}}$. Also, $\overline{BD} \cong \boldsymbol{\overline{DB}}$ by the Reflexive Property of Congruence
So, $\triangle ABD \cong \boldsymbol{\triangle CDB}$ by the SSS Congruence Theorem.