Question

statement\treason
1 bd = bc + cd\treason ?
2 eg = ef + fg\treason ?
3 bd = eg\tgiven
4 bc + cd = ef + fg\treason ?
5 bc = fg\tgiven
6 fg + cd = ef + fg\treason ?
7 cd = ef\treason ?

Explanation:

Step1: Segment - addition postulate

The whole segment is the sum of its parts, so $BD = BC + CD$ and $EG=EF + FG$.

Step2: Substitution property

Since $BD = EG$, $BC + CD$ can be substituted for $BD$ and $EF + FG$ for $EG$, so $BC + CD=EF + FG$.

Step3: Substitution property

Substitute $BC$ with $FG$ (as $BC = FG$ is given), getting $FG + CD=EF + FG$.

Step4: Subtraction property of equality

Subtract $FG$ from both sides of $FG + CD=EF + FG$, resulting in $CD = EF$.

Answer:

1. Segment - addition postulate
2. Segment - addition postulate
3. Given
4. Substitution property
5. Given
6. Substitution property
7. Subtraction property of equality