To prove BC = DE given BD = CE, use a two-column proof leveraging given information, Segment Addition Postulate, and the Properties of Equality for substitution and simplification.
To prove that BC = DE given that BD = CE within line BE, we can use a two-column proof structure that involves stating the facts, geometric theorems, or logical arguments side by side with their corresponding reasoning.
Statement: BD = CE (Given)
Statement: BD + DE = BE and BC + CE = BE (Reason: Segment Addition Postulate)
Statement: BD + DE = BC + CE (Reason: Both equal BE.)
Statement: Substitute BD = CE into the equation (BD + DE = BC + CE). (Reason: Substitution Property of Equality.)
Statement: CE + DE = BC + CE (Reason: Since BD = CE.)
Statement: Subtract CE from both sides. (Reason: Subtraction Property of Equality)
Statement: DE = BC (Reason: Simplification.)