Chapter 4.6, Problem 11WE

To determine

Prove $\overline{DH}\cong \overline{FK}$

Explanation of Solution

Given:

  $\overline{DE}\cong \overline{FG}$

  $\overline{GD}\cong \overline{EF}$

  $\angle HDE\text{ and }\angle \text{KFG }$ are right angles.

Calculation:

The diagram is :

  

Consider the $\Delta GDE\text{ and }\Delta EFG$ :

  $\overline{GD}\cong \overline{EF}$

  $\overline{DE}\cong \overline{FG}$

  $\overline{EE}\cong \overline{EG}$

So, by SSS Postulate , $\Delta GDE\cong \Delta EFG$

So, $\angle DEG\cong \angle FGE$

Consider the $\Delta HDE\text{ and }\Delta KFG$ :

  $\angle HDE\cong \angle \text{KFG }$

  $\overline{DE}\cong \overline{FG}$

  $\angle DEH\cong \angle FGK$

So, by ASA Postulate , $\Delta HDE\cong \Delta KFG$

Hence , $\overline{DH}\cong \overline{FK}$

Hence proved.