Question

part 2 of 3
complete the proof
given: $\angle b \cong \angle d$ and $\overline{ac} \cong \overline{ce}$
prove: $\triangle cab \cong \triangle ced$
complete the proof below
statement reason
$\angle b \cong \angle d$ and $\overline{ac} \cong \overline{ce}$ given
$\boldsymbol{\
abla}$ vertical angles theorem
$\angle bca \cong \angle dce$
$\angle acd \cong \angle dce$
$\angle bca \cong \angle cde$
$\angle acd \cong \angle cde$

Explanation:

Step1: Recall Vertical Angles Theorem

Vertical Angles Theorem states that vertical angles are congruent. In the diagram, $\angle BCA$ and $\angle DCE$ are vertical angles (formed by the intersection of lines $AE$ and $BD$ at point $C$). So the statement for the reason "Vertical Angles Theorem" should be $\angle BCA \cong \angle DCE$.

Step2: Verify the Statement

Looking at the options, the correct statement that follows from the Vertical Angles Theorem is $\angle BCA \cong \angle DCE$.

Answer:

$\boldsymbol{\angle BCA \cong \angle DCE}$