Chapter 8, Problem 4CT

To determine

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

Answer to Problem 4CT

NE is the geometric mean between DE and EF

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 NE and the hypotenuse is expressed as,

  

  $\begin{array}{l}N{E}^2=DE\times EF\\ NE=\sqrt{DE\times EF}\end{array}$

This implies NE is the geometric mean of the DE and EF