In the adjoining figure, PL ⊥ QR; LQ = LS and LR > LQ. Show that PR > PQ.

In the adjoining quadrilateral ABCD, AB is the longest side and DC is the shortest side. Prove that :

(i) ∠C > ∠A

(ii) ∠D > ∠B

In the adjoining figure, △ABC is equilateral and D is any point on AC. Prove that:

(i) BD > AD

(ii) BD > DC

If O is any point inside △ABC, prove that ∠BOC > ∠A.