Question

complete the proof by choosing the correct
eason\. given: bd = eg bc = fg prove: cd = ef step statement reason 1 bd = bc + cd reason? 2 eg = ef + fg reason? 3 bd = eg reason? 4 bc + cd = ef + fg reason? 5 bc = fg reason? 6 fg + cd = ef + fg reason? 7 cd = ef reason?

Explanation:

Step1: Segment - addition postulate

By the segment - addition postulate, a line segment can be written as the sum of its sub - segments. So, $BD = BC + CD$.

Step2: Segment - addition postulate

Similarly, by the segment - addition postulate, $EG=EF + FG$.

Step3: Given

The problem statement gives that $BD = EG$.

Step4: Substitution property of equality

Since $BD = BC + CD$, $EG=EF + FG$, and $BD = EG$, we substitute to get $BC + CD=EF + FG$.

Step5: Given

The problem statement gives that $BC = FG$.

Step6: Substitution property of equality

Substitute $BC$ with $FG$ in the equation $BC + CD=EF + FG$, we get $FG + CD=EF + FG$.

Step7: Subtraction property of equality

Subtract $FG$ from both sides of the equation $FG + CD=EF + FG$. So, $CD = EF$.

Answer:

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