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,

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a

y=3x+4

step-by-step explanation:

given the points a(0,4) and b(-4, -8)

eqn of line ab: (y-4)/(x-0)=(-8-4)/(-4-0)

(y-4)/x=-12/-4=3

y=3x+4