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DeanR

The altitude from the right angle of a right triangle makes two triangles that are similar to the original. That's proven by AA because they all have right angles and each shares an angle with the larger triangle.

r/h is the ratio of the short leg r to the long leg h of the smallest of these triangles.

For ?/s to be equal it must the ratio of the short leg ? to the long leg s. So ? is the short leg of the medium sized triangle, h.

[tex] \dfrac r h = \dfrac h s[/tex]

[tex]h^2 = rs[/tex]

The altitude is the geometric mean of the partitioned segments of the hypotenuse.

Answer: Last choice h

The complete proportion is [tex]\rm \dfrac{r}{h} = \dfrac{h}{s}[/tex].

Given that

Proportion; [tex]\rm \dfrac{r}{h} = \dfrac{?}{s}[/tex]

We have to complete the given proportion.

According to the question

In the given figure the required proportion is given by using the altitude rule;

An altitude is basically a perpendicular line segment that is drawn from a vertex of a triangle to the opposite side.

Then,

[tex]\rm \dfrac{Part \ of \ hypotenuse}{Part \ of \ altitude} = \dfrac{Part \ of \ hypotenuse}{Part \ of \ remaing \ hypotenuse}[/tex]

The part of the hypotenuse is r, the part of altitude is h, and the remaining part of the hypotenuse is s.

Substitute all the values in the proportion;

[tex]\rm \dfrac{Part \ of \ hypotenuse}{Part \ of \ altitude} = \dfrac{Part \ of \ altitude}{Part \ of \ remaing \ hypotenuse}\\\\\dfrac{r}{h} = \dfrac{h}{s}[/tex]

Hence, the complete proportion is [tex]\rm \dfrac{r}{h} = \dfrac{h}{s}[/tex].

To know more about Triangles click the link given below.

https://brainly.com/question/11475981

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