Question

geometry mod 1 test a1 25-26
true or false: if pq ≅ qr, with pq = 3x - 7, qr = 2x + 2, and rs = x + 9, then ps = 48.
p q r s
true
false

Explanation:

Step1: Set PQ equal to QR

Since $PQ\cong QR$, we have $3x - 7=2x + 2$.

Step2: Solve for x

Subtract $2x$ from both sides: $3x-2x - 7=2x-2x + 2$, which gives $x-7 = 2$. Then add 7 to both sides: $x=2 + 7=9$.

Step3: Find lengths of segments

$PQ=3x - 7=3\times9-7=27 - 7=20$. Since $PQ = QR$, $QR = 20$. $RS=x + 9=9+9 = 18$.

Step4: Calculate PS

$PS=PQ + QR+RS=20 + 20+18=58$.

Answer:

False