Question

decide whether the congruence statement is true. explain your reasoning
$\triangle def \cong \triangle dgf$

the congruence statement is \boxed{}? you are given that $overline{ef} \cong$ \boxed{} and $overline{de} \cong$ \boxed{} too. $overline{df} \cong$ \boxed{} by the \boxed{}. so, $\triangle def \cong$ \boxed{} by the sss congruence theorem.

Explanation:

1. First, identify the marked congruent sides: $\overline{EF} \cong \overline{GF}$ and $\overline{DE} \cong \overline{DG}$ from the diagram.
2. $\overline{DF}$ is a shared side, so $\overline{DF} \cong \overline{DF}$ by the Reflexive Property of Congruence.
3. By the SSS Congruence Theorem, all three pairs of corresponding sides are congruent, so $\triangle DEF \cong \triangle DGF$, making the original statement correct.

Answer:

The congruence statement is $\boldsymbol{\text{correct}}$. You are given that $\overline{EF} \cong \boldsymbol{\overline{GF}}$ and $\overline{DE} \cong \boldsymbol{\overline{DG}}$. Also, $\overline{DF} \cong \boldsymbol{\overline{DF}}$ by the $\boldsymbol{\text{Reflexive Property of Congruence}}$. So, $\triangle DEF \cong \boldsymbol{\triangle DGF}$ by the SSS Congruence Theorem.