Chapter 5.5, Problem 30PSC

To determine

To show: $\overline{HF}\cong \overline{DB}$ .

Explanation of Solution

Given information:

A solid box is given as below.

  

$▱ABCD\cong ▱EFHG$

Calculation:

A solid box is given as below.

  

  $\begin{array}{l}\text{In above figure,}\\ ▱ABCD\cong ▱EFHG\\ \overline{HE}\cong \overline{DA}\\ \overline{EF}\cong \overline{AB}\\ {\left(\overline{HE}\right)}^2+{\left(\overline{EF}\right)}^2={\left(\overline{DA}\right)}^2+{\left(\overline{AB}\right)}^2\\ \Rightarrow {\left(\overline{HF}\right)}^2={\left(\overline{DB}\right)}^2\\ \Rightarrow \overline{HF}=\overline{DB}\end{array}$