Problem

Complete the missing statement or reason in this proof step: \(AB=DE\), \(BC=EF\), \(\angle~B=\angle~E\), so \(\triangle~ABC~\cong~\triangle~DEF\) by .

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What this problem is really about

To fill a proof blank, classify each given as a side fact or an angle fact before naming any theorem. Then check the angle’s placement relative to the known sides; only after the evidence forms a valid pattern should you write the congruence statement and the reason that supports it.

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Triangle ABC is congruent to triangle DEF by the reflexive property because AB = DE, BC = EF, and angle B = angle E show matching parts.

Triangle ABC is congruent to triangle DEF by SSS because AB = DE, BC = EF, and angle B = angle E provide all three corresponding sides.

Triangle ABC is congruent to triangle DEF by SAS because AB = DE, BC = EF, and angle B = angle E give two sides and the included angle.

Triangle ABC is congruent to triangle DEF by ASA because AB = DE, BC = EF, and angle B = angle E give two angles and a side.

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Complete the missing statement or reason in this proof step: \(AB=DE\), \(BC=EF\), \(\angle~B=\angle~E\), so \(\triangle~ABC~\cong~\triangle~DEF\) by .

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