Question

select the correct answer.
\\( \overline { m n } \\) is the midsegment of the trapezoid \\( a b c d \\). what is the length of segment \\( \overline { a b } \\)?

a. 8
b. 9
c. 10
d. 14

Explanation:

Step1: Recall the midsegment formula for trapezoid

The formula for the midsegment \(MN\) of a trapezoid \(ABCD\) (where \(MN=\frac{AB + CD}{2}\))

Step2: Substitute the known values into the formula

Given \(MN = 7\) and \(CD=6\). Let \(AB=x\). Then \(7=\frac{x + 6}{2}\)

Step3: Solve the equation for \(x\)

Multiply both sides of the equation \(7=\frac{x + 6}{2}\) by \(2\): \(2\times7=x + 6\), so \(14=x + 6\). Subtract \(6\) from both sides: \(x=14 - 6=8\)

Answer:

A. 8