Question

given: df = eg. prove: de = fg. 1 df = de + ef. reason? 2 eg = ef + fg. reason? 3 df = eg. reason? 4 de + ef = ef + fg. reason? 5 de = fg. reason?

Explanation:

Step1: Given segment - addition

By the segment - addition postulate, if a point $E$ lies on a line segment $\overline{DF}$, then $DF = DE+EF$.

Step2: Given segment - addition

By the segment - addition postulate, if a point $F$ lies on a line segment $\overline{EG}$, then $EG = EF + FG$.

Step3: Substitute using given

Since $DF = EG$ (given), we can substitute the expressions for $DF$ and $EG$ from Step 1 and Step 2. So $DE + EF=EF + FG$.

Step4: Subtract $EF$ from both sides

Using the subtraction property of equality, if $a + b=b + c$, then $a + b−b=b + c−b$, so $DE=FG$.

Answer:

1. Reason: Segment - addition postulate
2. Reason: Segment - addition postulate
3. Reason: Substitution property of equality
4. Reason: Subtraction property of equality
5. Reason: Subtraction property of equality