Question

triangle abc and triangle xyz are similar right triangles. which proportion can be used to show that the slope of ac is equal to the slope of xz? $\frac{bc}{ac}=\frac{yz}{xy}$ $\frac{ab}{xy}=\frac{bc}{yz}$ $\frac{ab}{bc}=\frac{xy}{yz}$ $\frac{ac}{bc}=\frac{xz}{yz}$

Explanation:

Step1: Recall slope formula

The slope of a line segment in a right - triangle is the ratio of the vertical change (rise) to the horizontal change (run). For line segment $AC$, the slope $m_{AC}=\frac{AB}{BC}$, and for line segment $XZ$, the slope $m_{XZ}=\frac{XY}{YZ}$.

Step2: Use similarity of triangles

Since $\triangle ABC\sim\triangle XYZ$, the ratios of corresponding sides are equal. And the slopes of $AC$ and $XZ$ are equal when the ratio of the vertical side to the horizontal side of the two similar right - triangles are equal. That is, $\frac{AB}{BC}=\frac{XY}{YZ}$.

Answer:

$\frac{AB}{BC}=\frac{XY}{YZ}$