PLEASE HELP ASAP! WORTH 100 POINTS! WILL MARK BRAINLIEST!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. (4 points)

When an altitude is drawn perpendicular to the hypotenuse of a right triangle, it divides the right triangle into two similar triangles, and each of them are likewise similar to each of the original right triangle based on the altitude to the hypotenuse similarity theorem. The length of their corresponding sides are also proportional to each other.

Part A: A pair of similar triangles is ΔRSP ~ ΔQSP

Part B: We know that ΔRSP ~ ΔQSP based on the altitude to the hypotenuse similarity theorem.

Part C: Given the following,

RS = 4

RQ = 16

To find the length of segment RP (leg), use the leg rule:

Leg rule is expressed as hyp/leg = leg/part.

Hyp = RQ = 16

Leg = RP = ?

Part = RS = 4

Plug in the values

16/RP = RP/4

(RP)(RP) = (4)(16)

RP² = 64

RP = √64

RP = 8

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