Question

fall 2025 geometry b wwva
proving a quadrilateral is a parallelogram
in parallelogram pqsr, what is pq?
2 cm
6 cm
5 cm
9 cm

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite sides are equal. So, \(PQ = SR\). Given \(PQ=(2x + 5)\text{cm}\) and \(SR=(4x+1)\text{cm}\), we set up the equation \(2x + 5=4x + 1\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(5 = 2x+1\). Then subtract \(1\) from both sides: \(4 = 2x\). Divide by \(2\): \(x = 2\).

Step3: Find \(PQ\)

Substitute \(x = 2\) into \(PQ=2x + 5\). So \(PQ=2\times2+5=4 + 5=9\text{cm}\).

Answer:

\(9\text{cm}\)