Question

triangles abd and ace are similar right triangles. which ratio best explains why the slope of \\(\overline{ab}\\) is the same as the slope of \\(\overline{ac}\\)? \\(\frac{ac}{ea} = \frac{ab}{da}\\) \\(\frac{bd}{ba} = \frac{ce}{ca}\\) \\(\frac{bd}{da} = \frac{ce}{ea}\\) \\(\frac{bd}{da} = \frac{ea}{ce}\\)

Explanation:

Step1: Define slope for AB

Slope of $\overline{AB} = \frac{BD}{DA}$

Step2: Define slope for AC

Slope of $\overline{AC} = \frac{CE}{EA}$

Step3: Relate via similar triangles

For similar triangles, corresponding side ratios are equal. Since slopes are equal, their rise-over-run ratios match.

Answer:

$\boldsymbol{\frac{BD}{DA} = \frac{CE}{EA}}$ (third option)