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Seth is using the figure shown below to prove the Pythagorean Theorem using triangle similarity:

In the given triangle DEF, angle D is 90° and segment DG is perpendicular to segment EF.

Part A: Identify a pair of similar triangles. (2 points)

Part B: Explain how you know the triangles from Part A are similar. (4 points)

Part C: If EG = 2 and EF = 8, find the length of segment ED. Show your work. (4 points)

Seth is using the figure shown below to prove the Pythagorean Theorem using triangle similarity In the given triangle DEF angle D is 90 and segment DG is perpen class=

Respuesta :

Using the concept of similar triangles, we have that:

A. Triangles DGF and DGE are similar.

B. They are similar because they have the same angles.

C. [tex]ED = 2\sqrt{2}[/tex].

What are similar triangles?

Similar triangles are triangles that have the same angle measures, hence their side lengths have proportional measures.

In this problem, segment DG bisects triangle FDE, hence:

  • Angle EDG = Angle FDG = 45º.
  • Angle EGD = Angle FGD = 90º.
  • Angle E = Angle F = 45º.

Since they have the same angle measures, triangles DGF and DGE are similar.

To find ED, we consider that:

  • ED is the hypotenuse.
  • The adjacent side to the angle of 45º is of 2, hence:

[tex]\cos{45^\circ} = \frac{2}{ED}[/tex]

[tex]\frac{\sqrt{2}}{2} = \frac{2}{ED}[/tex]

[tex]ED = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]ED = 2\sqrt{2}[/tex].

More can be learned about similar triangles at https://brainly.com/question/305520

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