Chapter 8, Problem 5CT

To determine

To fill the blanks: with the appropriate name of the segments with reference to the given figure

Answer to Problem 5CT

NF is the geometric mean between EF and DF

Explanation of Solution

Given Information: A triangle with a right angle and a perpendicular directed to the hypotenuse.

For a right triangle NDF with a perpendicular NE being drawn to the hypotenuse DF (as shown below), the relation between the one of the legs of the bigger triangle and the normal to it is expressed as,

  

  $\begin{array}{l}N{F}^2=EF\times DF\\ NF=\sqrt{EF\times DF}\end{array}$

This implies NF is the geometric mean of the EF and DF