Question

step statement reason
1
ae || df
ae ≅ df
ab ≅ cd
given
2
∠a ≅ ∠d
parallel lines cut by a transversal form congruent alternate interior angles
3
type of statement
4
ac ≅ bd
congruent segments added to congruent segments form congruent segments
5
△eac ≅ △fdb
sas

Explanation:

Step1: Analyze the problem

We need to find the statement for step 3. Given that \(AB\cong CD\), if we add \(BC\) to both segments (\(AB + BC\) and \(CD+BC\)), we can get \(AC\) and \(BD\).

Step2: Determine the statement

Since \(AB + BC=AC\) and \(CD + BC = BD\) (segment addition postulate) and \(AB\cong CD\) (given), the statement for step 3 is \(BC\cong BC\) (reflexive property of congruence, which is used to show that when we add \(BC\) to \(AB\) and \(CD\) to get \(AC\) and \(BD\) respectively, the segment \(BC\) is common to both additions.

Answer:

\(BC\cong BC\)