Question

analyze the diagram below and complete the instructions that follow. determine if the proportion \\(\frac{e}{d} = \frac{d}{f}\\) is true. if it is not true, correct the error. a. true b. false, it should be \\(\frac{e}{d} = \frac{d}{h}\\) c. false, it should be \\(\frac{e}{d} = \frac{d}{g}\\) d. false, it should be \\(\frac{f}{d} = \frac{d}{f}\\)

Explanation:

Step1: Identify similar triangles

The diagram shows a right triangle with an altitude \(d\) to the hypotenuse, creating three similar right triangles: \(\triangle e-d-g \sim \triangle d-f-h \sim \triangle e-f-h\).

Step2: Set up proportional sides

For similar triangles, corresponding sides are proportional. In \(\triangle e-d-g\) and \(\triangle d-f-g\), the ratio of the hypotenuse to the shorter leg of the first triangle equals the ratio of the hypotenuse to the shorter leg of the second triangle:
$$\frac{e}{d} = \frac{d}{f}$$

Step3: Verify the proportion

The given proportion matches the proportionality derived from similar triangles, so it is true.

Answer:

A. true