Question

based on the following proof, what statement goes into where statement 2 should go?
given: (overline{bc}=overline{dc};overline{ac}=overline{ec})
prove: (\triangle bca=\triangle dce)

1. (overline{bc}=overline{dc};overline{ac}=overline{ec}) 1. given
2. 2. vertical (angle s) theorem
3. (\triangle bca=\triangle dce) 3. sas

(angle bcongangle d)
(angle bcacongangle dce)

Explanation:

Step1: Analyze the Reason for Statement 2

The reason for statement 2 is "Vertical ∠s Theorem". This theorem is used to state that two angles are congruent when they are vertical angles. In the context of proving triangle congruence, we need to identify which pair of angles are vertical angles.

Step2: Identify the Vertical Angles

Looking at the triangles \( \triangle BCA\) and \( \triangle DCE\), the angles \( \angle BCA\) and \( \angle DCE\) are vertical angles. By the Vertical Angles Theorem, vertical angles are congruent.

Answer:

\(\angle BCA\cong\angle DCE\)