Question

question 4 of 5
given: ad = cf
bc = de
prove: ab = ef
statement

1. ad = cf
2. ad = ab + bc + cd

cf = cd + de + ef

1. ab + bc + cd = cd + de + ef
2. ab + bc = de + ef
3. bc = de

Explanation:

Step1: Substitute \(BC\) with \(DE\)

Since \(BC = DE\) (given), substitute \(BC\) in \(AB + BC=DE + EF\). We get \(AB+DE = DE + EF\).

Step2: Subtract \(DE\) from both sides

Using the subtraction property of equality, if \(a + b=b + c\), then \(a=c\). For \(AB+DE = DE + EF\), subtract \(DE\) from both sides: \(AB+DE-DE=DE + EF - DE\).

Answer:

\(AB = EF\)