In the given figure, PR > PQ

Prove that : AR > AQ.

Given: PR > PQ

To prove : AR > AQ.

Proof : PR > PQ (Given)

As we know that angle opposite to greater side is always greater.

⇒ ∠PAR > ∠PAQ

In Δ QAP,

Sum of all angles of the triangle is 180°.

⇒ ∠PAQ + ∠APQ + ∠AQP = 180° ………….(1)

Similarly, in Δ RAP,

Sum of all angles of the triangle is 180°.

⇒ ∠PAR + ∠APR + ∠ARP = 180° ………….(2)

From (1) and (2),

⇒ ∠PAR + ∠APR + ∠ARP = ∠PAQ + ∠APQ + ∠AQP

⇒ ∠PAR + 90° + ∠ARP = ∠PAQ + 90° + ∠AQP

⇒ ∠PAR + ∠ARP = ∠PAQ + ∠AQP

As we know ∠PAR > ∠PAQ,

So, ∠AQP > ∠ARP

And, side opposite to greater angle is always greater.

Hence, AR > AQ.