Question

complete the proof by choosing the correct
eason\. given: be = df, ce = ef. prove: bc = de. step statement reason 1 be = bc + ce reason? 2 df = de + ef reason? 3 be = df reason? 4 bc + ce = de + ef reason? 5 ce = ef reason? 6 bc + ef = de + ef reason? 7 bc = de reason?

Explanation:

Step1: Segment - addition postulate

$BE = BC + CE$ (The whole segment $BE$ is the sum of its parts $BC$ and $CE$)

Step2: Segment - addition postulate

$DF=DE + EF$ (The whole segment $DF$ is the sum of its parts $DE$ and $EF$)

Step3: Given

$BE = DF$ (Given in the problem statement)

Step4: Substitution property of equality

Since $BE = BC + CE$ and $DF=DE + EF$ and $BE = DF$, then $BC + CE=DE + EF$

Step5: Given

$CE = EF$ (Given in the problem statement)

Step6: Substitution property of equality

Substitute $CE$ with $EF$ in $BC + CE=DE + EF$, getting $BC + EF=DE + EF$

Step7: Subtraction property of equality

Subtract $EF$ from both sides of $BC + EF=DE + EF$, resulting in $BC = DE$

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