Question

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

Explanation:

Step1: Segment - addition postulate

$AC = AB + BC$ because a line - segment is the sum of its parts.

Step2: Segment - addition postulate

$DF = DE+EF$ for the same reason that a line - segment is the sum of its parts.

Step3: Given

$AC = DF$ is given in the problem statement.

Step4: Substitution property

Since $AC = AB + BC$ and $DF = DE + EF$ and $AC = DF$, we substitute to get $AB + BC=DE + EF$.

Step5: Given

$BC = DE$ is given in the problem statement.

Step6: Substitution property

Substitute $BC$ with $DE$ in $AB + BC=DE + EF$ to get $AB + DE=DE + EF$.

Step7: Subtraction property of equality

Subtract $DE$ from both sides of $AB + DE=DE + EF$. So $AB=EF$.

Answer:

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