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

In the given triangle PQR, angle P is 90° and segment PS is perpendicular to segment QR.

The figure shows triangle PQR with right angle at P and segment PS. Point S is on side QR.

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 RS = 4 and RQ = 16, find the length of segment RP. Show your work.

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ogorwyne

The answers to the question are:

  • ΔRSP ~ ΔQSP
  • The triangles are similar based on the hypotenuse similarity theorem and the hypotenuse.
  • The segment of RP is 8

How to solve for the Hypotenuse Similarity Theorem

A perpendicular hypotenuse to the right triangle is a line that is capable of dividing the right angled triangle to become the same triangles or similar triangles. The similarity of the triangles are based on its altitudes. With the lengths of the side corresponding to the proportionality.

We have the following ΔRSP ~ ΔQSP

The data that we have in the question are as follows RS = 4 and RQ = 16

We are to use the leg rule in order to get the segment

the formula is hyp/leg = leg/part.

RQ = hyp = 16 and the value of the leg is unknown

RS is 4

We have to put in the values

16/RP = RP/4

Cross multiply

16*4 = RP*RP

64 = RP²

Squared both sides

8 = RP

Read more on segments here: https://brainly.com/question/27817733?referrer=searchResults

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