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)

Step-by-step explanation:

I assume the figure is the one attached below.

One pair of similar triangle is ΔRSP and ΔRPQ.

We know this because ∠R = ∠R, and ∠S = ∠P (both are right angles).  Therefore, by AA similarity, the triangles must be similar.

Using the similarity statement, we can write and solve a proportion:

RS / RP = RP / RQ

4 / RP = RP / 16

64 = RP²

RP = 8

the right system of equations to describe the situation would

be on the form:

x1 = 8000 + y1*t

and

x2 = 8000 + y2*t

where x1 and x2 represents the total money of imogene and her

friend respectively at the end of t years.

now for the value of amount earned, y1 and y2:

y1=8000*0.08

y2=2000*√(t-2)

linear pair postulates