Question

find the length of \\( \overline{cd} \\). the length of \\( \overline{be} \\) is 18 in.

Explanation:

Step1: Identify Midsegment

From the markings, \( B \) is the midpoint of \( AC \) and \( E \) is the midpoint of \( AD \). So, \( BE \) is the midsegment of \( \triangle ACD \).

Step2: Apply Midsegment Theorem

The Midsegment Theorem states that the midsegment of a triangle is parallel to the third side and half its length. So, \( BE=\frac{1}{2}CD \).

Step3: Solve for \( CD \)

Given \( BE = 18 \) in, we substitute into the formula: \( 18=\frac{1}{2}CD \). Multiply both sides by 2: \( CD = 18\times2 = 36 \) in.

Answer:

The length of \( \overline{CD} \) is 36 inches.