Question

in the figure below, there are three right trangles. complete the following. (a) write a similarity statement relating the three right triangles. △wyx - △ - △ (b) complete each proportion. $\frac{zx}{yx}=\frac{yx}{}$ $\frac{wz}{yz}=\frac{}{zx}$

Explanation:

Step1: Identify similar right - triangles

In a right - triangle with an altitude drawn to the hypotenuse, the three right - triangles formed are similar. In right - triangle $WYX$ with altitude $YZ$, $\triangle WYX\sim\triangle YZX\sim\triangle WZY$.

Step2: Use the property of similar triangles for proportions

For similar triangles, the ratios of corresponding sides are equal. In $\triangle YZX$ and $\triangle WYX$, $\frac{ZX}{YX}=\frac{YX}{WX}$ because corresponding sides of similar triangles are in proportion. In $\triangle WZY$ and $\triangle YZX$, since they are similar, $\frac{WZ}{YZ}=\frac{YZ}{ZX}$.

Answer:

(a) $\triangle WYX\sim\triangle YZX\sim\triangle WZY$
(b) $\frac{ZX}{YX}=\frac{YX}{WX}$, $\frac{WZ}{YZ}=\frac{YZ}{ZX}$