Question

proving a quadrilateral is a parallelogram
in parallelogram abcd, what is dc?
3 in.
13 in.
19 in.
9 in.

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, \(AB = DC\). Given \(AB=(9x - 14)\) in and \(DC=(3x + 4)\) in. Then \(9x-14=3x + 4\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(9x-3x-14=3x-3x + 4\), which simplifies to \(6x-14 = 4\).
Add \(14\) to both sides: \(6x-14 + 14=4 + 14\), so \(6x=18\).
Divide both sides by \(6\): \(x=\frac{18}{6}=3\).

Step3: Find the length of \(DC\)

Substitute \(x = 3\) into the expression for \(DC\). \(DC=3x+4\).
\(DC=3\times3 + 4=9 + 4=13\) in.

Answer:

13 in.