Question

complete the proof by choosing the correct
eason\. given: $qs = tv$, $rs = tu$. prove: $qr = uv$. statement reason 1 $qs = qr + rs$ reason? 2 $tv = tu + uv$ reason? 3 $qs = tv$ reason? 4 $qr + rs = tu + uv$ reason? 5 $rs = tu$ reason? 6 $qr + tu = tu + uv$ reason? 7 $qr = uv$ reason?

Explanation:

Step1: Segment - addition postulate

$QS = QR+RS$ because a line - segment can be written as the sum of its non - overlapping sub - segments.

Step2: Segment - addition postulate

$TV = TU + UV$ for the same reason that a line - segment can be written as the sum of its non - overlapping sub - segments.

Step3: Given

It is given in the problem statement that $QS = TV$.

Step4: Substitution property of equality

Since $QS = QR + RS$, $TV = TU+UV$, and $QS = TV$, we substitute $QS$ with $QR + RS$ and $TV$ with $TU + UV$ to get $QR + RS=TU + UV$.

Step5: Given

It is given in the problem statement that $RS = TU$.

Step6: Substitution property of equality

Substitute $RS$ with $TU$ in the equation $QR + RS=TU + UV$ to get $QR + TU=TU + UV$.

Step7: Subtraction property of equality

Subtract $TU$ from both sides of the equation $QR + TU=TU + UV$. So, $QR=UV$.

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