Question

1. refer to the figure to complete the proportion.

\\(\frac{b}{x}=\frac{?}{b}\\)

Explanation:

Step1: Recall similar - triangles property

In a right - triangle with an altitude drawn to the hypotenuse, the two smaller right - triangles formed are similar to the large right - triangle and to each other. Consider the two right - triangles with sides \(b\) and \(x\) and \(b\) and the unknown side. The right - triangle with sides \(b\) and \(x\) and the large right - triangle with hypotenuse \(c\) and sides \(a\) and \(b\) are similar.
We know that if two triangles are similar, the ratios of their corresponding sides are equal.
The proportion \(\frac{b}{x}=\frac{c}{b}\) comes from the similarity of the right - triangles formed by the altitude \(h\) in the right - triangle with hypotenuse \(c\).

Answer:

c