Question

what do the triangles tell you about the slope? complete each statement. the triangles are congruent. the ratios of the corresponding side lengths are the same. the slope of each part of the line is the same. which quotient shows how to use \\( \triangle abe \\) to find the slope of the line? \\( \frac{be}{ab} \\) \\( \frac{ab}{ae} \\) \\( \frac{be}{ae} \\) \\( \frac{ae}{be} \\)

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{\text{rise}}{\text{run}}\). In \(\triangle ABE\), \(BE\) is the vertical side (rise) and \(AE\) is the horizontal side (run).

Step2: Apply the formula to the triangle

The slope \(m\) using \(\triangle ABE\) is given by the quotient of the vertical side length over the horizontal side length. So the quotient is \(\frac{BE}{AE}\).

Answer:

\(\frac{BE}{AE}\)