Question

parallelograms
using the parallelogram diagonal theorem
what is the length of segment eb in parallelogram abcd?
34.5 units
30 units
69 units

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(DE = EB\) and \(AE=EC\). Here, we can use \(2x + 9=3x - 21\) (since \(DE = EB\) in terms of the given expressions for the segments of the diagonals).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find the length of \(EB\)

Substitute \(x = 30\) into the expression for \(EB\) (\(3x-21\)). Then \(EB=3\times30 - 21=90 - 21 = 69\)

Answer:

69 units