Question

1. refer to the figure to complete this proportion.

\\(\frac{h}{a}=\frac{a}{?}\\)

Explanation:

Step1: Recall similar - triangles property

In a right - triangle with altitude \(h\) drawn to the hypotenuse \(c\), we have similar right - triangles. The two smaller right - triangles formed are similar to the large right - triangle and to each other. For the proportion \(\frac{h}{a}=\frac{a}{?}\), we use the geometric mean theorem in right - triangles.

Step2: Identify the corresponding side

By the geometric mean theorem in a right - triangle, if an altitude \(h\) is drawn to the hypotenuse \(c\) of a right - triangle, then \(h^{2}=r\times s\) and \(a^{2}=r\times c\), \(b^{2}=s\times c\). In the proportion \(\frac{h}{a}=\frac{a}{c}\), because of the similarity of triangles. The side corresponding to \(h\) in the larger triangle related to side \(a\) is the hypotenuse \(c\) of the large right - triangle.

Answer:

c