Question

if qt = 45 and pu = 56, what is rs?
rs = \square

Explanation:

Step1: Identify the Midline Theorem (Trapezoid Midsegment)

In a trapezoid, the midsegment (or midline) is parallel to the two bases and its length is the average of the lengths of the two bases. Here, \( QT \) is the midline, \( RS \) and \( PU \) are the two bases. The formula for the midline \( QT \) is \( QT=\frac{RS + PU}{2} \).

Step2: Substitute the Known Values

We know \( QT = 45 \) and \( PU = 56 \). Substitute these values into the formula: \( 45=\frac{RS + 56}{2} \).

Step3: Solve for \( RS \)

Multiply both sides of the equation by 2: \( 45\times2=RS + 56 \), which simplifies to \( 90=RS + 56 \). Then subtract 56 from both sides: \( RS=90 - 56 \).

Step4: Calculate the Result

\( 90-56 = 34 \).

Answer:

\( 34 \)