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)

A.

B. All angles are same, so the triangles are similar.

C. RP = 8

Step-by-step explanation:

Given right angled in which

Line segment PS is perpendicular to QR and S is on the line QR.

Kindly refer to the attached diagram for the given dimensions and angles.

Part A.

Part B. Let us consider the two triangles: .

and is common to both the triangles.

Two angles of two triangles are equal to other other.

So, third angle will also be equal to each other.

by AAA similarity:

Part C:

The ratio of corresponding sides of two triangles is equal.

So,