Chapter 11, Problem 8CUR

To determine

To state: The statement is true / false.

Answer to Problem 8CUR

False

Explanation of Solution

Given:

Altitude to hypotenuse of a right triangle.

Geometric mean of two numbers $a,b$ is equal to $\sqrt{ab}$ .

The given statement can be plotted as the image shown below:

  

$BD$ is the altitude to the hypotenuse $AC$ of the right $\Delta ABC$ .

As per altitude geometric mean theorem, the altitude to hypotenuse of a right triangle is equal to the geometric mean of the segments of hypotenuse divided by the altitude to hypotenuse.

i.e.

  $BD=\sqrt{xy}$

Therefore, the given statement is false.