Question

A student made the table below to show the steps to prove that DC is equal to EC.

Statements Justifications

AC = BC

Given

m∡EAC = m∡DBC

Given

m∡ACD = m∡BCE

Given

m∡ACE = m∡ACD + m∡DCE

Angle Addition Postulate

m∡BCD = m∡BCE + m∡DCE

Angle Addition Postulate

m∡BCD = m∡ACD + m∡DCE

Substitution



triangleDBC≅ triangleEAC

ASA postulate

DC = EC

CPCTC


A. Provide the missing statement and justification in the proof.
B. Using complete sentences, explain why the proof would not work without the missing step