Question

1. if $pq = 9$ and $qr = 28$, find $pr$.
2. if $qr = 17$ and $pr = 21$, find $pq$.

Explanation:

Step1: Use segment - addition postulate

Assume that point Q lies on line segment PR. Then $PR = PQ+QR$.

Step2: Solve for PR in the first case

Given $PQ = 9$ and $QR = 28$, substitute into the formula: $PR=9 + 28$.
$PR=37$

Step3: Rearrange the formula for the second case

Since $PR = PQ+QR$, we can rewrite it as $PQ=PR - QR$.

Step4: Solve for PQ in the second case

Given $QR = 17$ and $PR = 21$, substitute into the formula: $PQ=21 - 17$.
$PQ = 4$

Answer:

1. $PR = 37$
2. $PQ = 4$