Question

identifying a proportion
which proportion satisfies the geometric mean (altitude) theorem for the triangle?
\\( \frac { 2 } { n } = \frac { n } { 3 } \\)
\\( \frac { 2 } { n } = \frac { n } { n } \\)
\\( \frac { 2 } { n } = \frac { 3 } { n } \\)
\\( \frac { 2 } { n } = \frac { 3 } { m } \\)

Explanation:

Step1: Recall the geometric mean (altitude) theorem

In a right - triangle, if an altitude \(h\) is drawn to the hypotenuse, then \(h^{2}=\text{product of the segments of the hypotenuse}\). Also, for the geometric mean (altitude) theorem in a right - triangle formed by the altitude \(h\) to the hypotenuse, the proportion is \(\frac{2}{h}=\frac{h}{3}\) (where \(2\) and \(3\) are the segments of the hypotenuse and \(h\) is the altitude).

Answer:

\(\frac{2}{h}=\frac{h}{3}\)