Question

points p, q, r, and s are collinear. point q is between p and r, r is between q and s, and $overline{pq}congoverline{rs}$. if $ps = 32$ and $pr = 24$, what is the value of $qr$?
qr =
(simplify your answer.)

Explanation:

Step1: Define segment - length relationships

Since $P$, $Q$, $R$, $S$ are collinear and $PS = 32$, $PR = 24$, we know that $PS=PR + RS$. So, $RS=PS - PR$.
$RS = 32 - 24=8$.

Step2: Use the congruence property

Given $\overline{PQ}\cong\overline{RS}$, then $PQ = RS = 8$.

Step3: Find the length of $QR$

Since $PR=PQ + QR$, then $QR=PR - PQ$.
$QR = 24 - 8 = 16$.

Answer:

$16$