Question

step statement reason
1 ( overline{ab} cong overline{cd} ) ( overline{bc} cong overline{ad} ) given
2 ( overline{ac} cong overline{ac} ) reflexive property
3 ( \triangle abc cong \triangle cda ) sss
4 ( angle bca cong angle cad ) corresponding parts of congruent triangles are congruent (cpctc)
5 ( angle bec cong angle dea ) vertical angles are congruent
6 ( be cong ed ) corresponding parts of congruent triangles are congruent (cpctc)
7 ( overline{ac} ) bisects ( overline{bd} ) a segment bisector intersects the segment to form two congruent segments
note: ( overline{ac} ) and ( overline{bd} ) are segments.
answer attempt 1 out of 5
the proof is incorrect and step number is the first unjustified step due to a missing prior step

Explanation:

Step1: Analyze congruent triangles

We have \(\triangle ABC\cong\triangle CDA\) by SSS (Side - Side - Side) congruence criterion since \(AB = CD\), \(BC=AD\), and \(AC = AC\) (reflexive property).

Step2: Check for \(\angle BCA\cong\angle CAD\)

From \(\triangle ABC\cong\triangle CDA\), by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \(\angle BCA\cong\angle CAD\).

Step3: Analyze \(\angle BEC\cong\angle DEA\)

Vertical angles are congruent, so \(\angle BEC\cong\angle DEA\).

Step4: Check for \(BE\cong ED\)

To use CPCTC for \(BE\cong ED\), we need to show that \(\triangle BEC\cong\triangle DEA\). We have \(\angle BCA\cong\angle CAD\) (from step 4), \(\angle BEC\cong\angle DEA\) (from step 5), but we are missing a side - angle - side (SAS) or angle - side - angle (ASA) or side - side - side (SSS) congruence for \(\triangle BEC\) and \(\triangle DEA\). The first step where an unjustified claim is made for congruent triangles (to use CPCTC for \(BE\cong ED\)) is step 6.

Answer:

6