Given the figure on the left below with angle measures as marked. Prove that PR is the longest segment.

Question

Answer 1

From ΔPRK PR > PK And PR > RK.

Now from ΔPMK PK > PM and PK > KM

So, PR > PK, PR > KM, PR > PM and PR > RK.

We use here property of triangle (across bigger anle is bigger side) and transitive properties of inequality.

Answer 2

PK > MK > PM

PR > PK > RK