Question

use the given information to prove that ( bc = de ).
given: ( bd = ce )
prove: ( bc = de )

Explanation:

Step1: Express \(BD\) and \(CE\) in terms of segments

From the line - segment \(B - C - D - E\), we know that \(BD=BC + CD\) and \(CE=CD + DE\) (Segment Addition Postulate).

Step2: Substitute into the given equation

Since \(BD = CE\) (given), substitute \(BD\) and \(CE\) from Step 1: \(BC + CD=CD + DE\).

Step3: Subtract \(CD\) from both sides

Using the Subtraction Property of Equality (\(a + c=b + c\Rightarrow a = b\)), if we subtract \(CD\) from both sides of \(BC + CD=CD + DE\), we get \(BC=DE\).

Answer:

\(BC = DE\) is proved.