Question

triangle ade is similar to triangle abc. which statement is true concerning the slope of the line formed by the hypotenuse of each triangle?

Explanation:

Step1: Recall slope formula

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For similar triangles, the ratios of corresponding sides are equal.

Step2: Analyze slope of hypotenuse

The slope of the line formed by the hypotenuse of similar triangles is the same. This is because the ratio of the vertical change (rise) to the horizontal change (run) is the same for similar triangles. If we consider $\triangle ADE$ and $\triangle ABC$, the ratio of the height to the base of both triangles (which gives the slope of the hypotenuse) is equal due to similarity.

Answer:

The slope of the line formed by the hypotenuse of $\triangle ADE$ is equal to the slope of the line formed by the hypotenuse of $\triangle ABC$.