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Two Column Proof: Given: BD = CE Prove: BC = DE

Two Column Proof: Given: BD = CE Prove: BC = DE-example-1

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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.)

User Miles Elam
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