Chapter 5.5, Problem 31WE

To determine

ToProve: that $EF=\frac{1}{2}\left(AB-DC\right)$ shown in figure such that ABCD is trapezoid with median MN.

Explanation of Solution

Given

Figure is shown as.

  

ABCD is trapezoid with median MN.

Proof:

Since, MN is a median therefore.

  $ME=\frac{1}{2}DC\mathrm{.......}\left(1\right)$

  $MF=\frac{1}{2}AB\mathrm{.......}\left(2\right)$

Now,

  $\begin{array}{l}EF=MF-ME\\ EF=\frac{1}{2}AB-\frac{1}{2}DC\\ EF=\frac{1}{2}\left(AB-DC\right)\end{array}$