Question

f - e = f - e
\frac{f}{e} = \frac{f}{e}
slope cannot be a ratio.
statement\treason
slope from p to q = \frac{f}{e}\tdefinition of slope
slope from q to r = \frac{f}{e}\tdefinition of slope
\ttriangle 1 is similar to triangle 2.

Explanation:

Step1: Recall the property of similar triangles

When two triangles are similar, their corresponding sides are proportional. So if triangle 1 (related to slope from \(P\) to \(Q\)) and triangle 2 (related to slope from \(Q\) to \(R\)) are similar, then \(\frac{F'}{E'}=\frac{F}{E}\) because the ratios of corresponding sides (which represent the slope, a ratio of rise over run) should be equal.

Step2: Analyze the other options

• The equation \(F - E=F' - E'\) is not related to the proportionality of slopes from similar triangles.
• The statement "Slope cannot be a ratio" is incorrect because slope is defined as the ratio of the vertical change to the horizontal change (\(\frac{\text{rise}}{\text{run}}\)).

So the correct item to drag for the reason "Triangle 1 is similar to triangle 2" is \(\frac{F'}{E'}=\frac{F}{E}\).

Answer:

\(\boldsymbol{\frac{F'}{E'}=\frac{F}{E}}\)