Question

fall 2025 geometry b wwva
proving a quadrilateral is a parallelogram
is parallelogram lonm, what is om?
24 cm
34 cm
7 cm
17 cm

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, \(OQ = QM\).
Given \(OQ=(2x + 3)\text{ cm}\) and \(QM=(3x - 4)\text{ cm}\), we set up the equation \(2x+3 = 3x - 4\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(3=x - 4\).
Add \(4\) to both sides: \(x=7\).

Step3: Find the length of \(QM\)

Substitute \(x = 7\) into \(QM=(3x - 4)\).
\(QM=3\times7-4=21 - 4=17\text{ cm}\).

Step4: Find the length of \(OM\)

Since \(OM = 2\times QM\) (because the diagonal is bisected), \(OM=2\times17 = 34\text{ cm}\).

Answer:

\(34\text{ cm}\)