Chapter 5, Problem 20RP

To determine

Prove that the figure is a parallelogram.

Answer to Problem 20RP

  $EFGH$ is a parallelogram.

Explanation of Solution

Given information:

The figure produced by joining the consecutive midpoint of a parallelogram.

Calculation:

Construct the figure as per the given statement,

  

  $\begin{array}{l}Fismidpo\mathrm{int}of\overline{BC},Gismidpo\mathrm{int}of\overline{CD}\\ Hismidpo\mathrm{int}of\overline{AD},Eismidpo\mathrm{int}of\overline{AB}\end{array}$

  $\begin{array}{l}\overline{FG}\left|\right|\overline{BD}\text{}\text{}\\ FG=\frac{1}{2}BD\left[midlinetheorem\right]\\ \overline{EH}\left|\right|\overline{BD}\text{}\text{}\\ EH=\frac{1}{2}BD\left[midlinetheorem\right]\\ \overline{FG}\left|\right|\overline{EH}\\ FG=EH\text{}\\ EFGHisparalle\log ram.\end{array}$

Hence, $EFGH$ is a parallelogram.