Question

step statement reason
\\( \angle b c f \cong \angle d c f \\)
\\( \overline{b c} \cong \overline{d c} \\)
1 \\( c \\) is the midpoint of \\( \overline{a e} \\) given
\\( \angle a c f \\) is a right angle
\\( \angle e c f \\) is a right angle
2 \\( \angle e c d \\) and \\( \angle d c f \\) are complementary if two angles form a right angle, then they are complementary
3 \\( \angle a c b \cong \angle e c d \\) if two angles are complements of the same angle (or congruent angles), then they are congruent
4 \\( \overline{a c} \cong \overline{c e} \\) a midpoint divides a segment into two congruent segments
5 \\( \triangle a c b \cong \triangle e c d \\) sas
note: \\( \overline{a e} \\) is a segment.
answer attempt 1 out of x
the proof is incorrect - and step number is the first unjustified step due to a missing prior step

Explanation:

Step1: Analyze Step 2

In Step 2, the reason is about complementary angles. But there is no prior step establishing that \(\angle ECD\) and \(\angle DCF\) form a right - angle. The right - angle given is \(\angle ECF\) (from the given \(\angle ECF\) is a right angle in Step 1). To use the "If two angles form a right angle, then they are complementary" reason, we need to show that \(\angle ECD+\angle DCF = 90^{\circ}\). Since \(\angle ECF=\angle ECD+\angle DCF\) (by angle addition postulate, which is a missing step), Step 2 is unjustified without first stating the angle - addition relationship.

Step2: Check other steps

Step 3: If we assume Step 2 was justified (after adding the angle - addition step), then for \(\angle ACB\cong\angle ECD\), we know \(\angle ACB + \angle BCF=90^{\circ}\) (because \(\angle ACF\) is a right angle) and if \(\angle ECD+\angle DCF = 90^{\circ}\) and \(\angle BCF\cong\angle DCF\) (given), then by the "If two angles are complements of the same angle (or congruent angles), then they are congruent" reason, Step 3 could be justified.
Step 4: Since \(C\) is the mid - point of \(\overline{AE}\) (given in Step 1), by the definition of a mid - point (\(AC = CE\)), \(\overline{AC}\cong\overline{CE}\) is justified.
Step 5: For \(\triangle ACB\cong\triangle ECD\) (SAS), we need two sides and the included angle. We have \(\overline{AC}\cong\overline{CE}\) (Step 4), \(\angle ACB\cong\angle ECD\) (Step 3), but we also need \(\overline{BC}\cong\overline{DC}\) (given in the problem statement at the top). However, the non - justification starts at Step 2.

Answer:

The first unjustified step is step number \(2\).